PAG

Question 1

Free fall experiment

Answer 1

Method and Calculations

• Measure the height (h):
  
  • Measure the vertical distance from the bottom of the ball bearing to the trapdoor.
• Release the ball bearing:
  
  • Simultaneously start the timer and disconnect the electromagnet by flicking the switch.
  • The ball bearing falls, knocking the trapdoor down, breaking the circuit, and stopping the timer.
• Record and repeat:
  
  • Record the time (t) shown on the timer.
  • Repeat the experiment three times and calculate the average time.
• Calculate acceleration due to gravity (g):
  
  • Use the equation: h = 0.5 * g * t² (from page 50).
  • Rearrange to solve for g = 2h / t².
• Repeat for different heights:
  
  • Perform the experiment for several heights, calculate g for each, and average the results.

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Analysis (y = mx + c)

• Plot a graph:
  
  • Plot h (y-axis) against t² (x-axis).
  • The graph should be linear, with the equation h = 0.5g * t², corresponding to y = mx + c, where:
    
    • Gradient (m) = 0.5g.
    • y-intercept (c) = 0.
• Determine g:
  
  • Calculate g = 2 * gradient.

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Accuracy, Safety, Limitations, and Improvements

• Accuracy:
  
  • Use a ruler with a high resolution to measure height (h) accurately.
  • Ensure the timer is precise and starts/stops exactly when the ball bearing is released/hits the trapdoor.
  • Repeat the experiment multiple times to reduce random errors.
• Safety:
  
  • Place a cushion or soft material below the trapdoor to prevent damage or injury from the falling ball bearing.
• Limitations:
  
  • Air resistance may affect the motion of the ball bearing, especially at higher heights.
  • Human reaction time may introduce errors when starting/stopping the timer manually.
  • The trapdoor mechanism may not break the circuit instantaneously.
• Improvements:
  
  • Use a light gate or electronic sensor to measure time more accurately.
  • Perform the experiment in a vacuum to eliminate air resistance.
  • Use a data logger to automatically record the time and reduce human error.

Question 2

Young’s Modulus (PAG)

Answer 2

Method and Calculations

• Set up the wire:
  
  • Use a thin and long test wire for more accurate measurements, reducing uncertainty.
  • Clamp the wire to the bench and hang weights off one end, starting with the smallest weight necessary to straighten the wire.
• Measure dimensions:
  
  • Find the wire’s cross-sectional area by measuring its diameter with a micrometer and using the formula for the area of a circle.
  • Measure the unstretched length from the fixed end of the wire to the marker.
• Record extensions:
  
  • Record the starting position of the marker.
  • Increase the weight in steps and record the marker reading each time to determine the extension.
• Calculate stress and strain:
  
  • Use the results to calculate stress and strain of the wire.
  • Plot a stress-strain curve.

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Analysis (y = mx + c)

• Plot a graph:
  
  • Plot stress (y-axis) against strain (x-axis).
  • The graph should show a linear region (Hooke’s Law) where stress ∝ strain, corresponding to y = mx + c, where:
    
    • Gradient (m) = Young’s modulus.
    • y-intercept (c) = 0.

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Accuracy, Safety, Limitations, and Improvements

• Systematic Errors:
  
  • Use a vernier scale for more precise readings of extension.
  • Ensure the wire returns to its original length after removing the load to avoid permanent deformation.
• Random Errors:
  
  • Reduce parallax error by reading the marker carefully.
  • Repeat the experiment for all loads and calculate an average extension.
  • Measure the wire’s diameter at several points and take an average to reduce uncertainty in cross-sectional area.
• Safety Considerations:
  
  • Wear safety goggles in case the wire snaps.
  • Place a cushion or soft surface below the mass hanger to catch it if it falls.
• Improvements:
  
  • Use a digital micrometer for more accurate diameter measurements.
  • Ensure the wire is perfectly vertical to avoid uneven stretching.
  • Use a data logger to automatically record extensions for greater precision.

Question 3

Resistivity (PAG)

Answer 3

Method and Calculations

• Measure the wire dimensions:
  
  • Measure the diameter of the wire in at least three places and calculate the mean diameter.
  • Halve the mean diameter to find the mean radius.
  • Use the radius to calculate the cross-sectional area (A = πr²).
• Set up the experiment:
  
  • Clamp the wire and attach the flying lead.
  • Close the switch and measure the current (I) and potential difference (V) across the test wire.
  • Calculate the resistance (R) using R = V/I.
• Repeat for different lengths:
  
  • Reposition the flying lead for different wire lengths and repeat the process.
  • Record the mean resistance for each length.

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Analysis (y = mx + c)

• Plot a graph:
  
  • Plot average resistance (y-axis) against length (x-axis).
  • The graph should be linear, with the equation R = (ρ/A) * L, corresponding to y = mx + c, where:
    
    • Gradient (m) = ρ/A.
    • y-intercept (c) = 0.
• Determine resistivity:
  
  • Calculate ρ = gradient × A, where A is the cross-sectional area.

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Accuracy, Safety, Limitations, and Improvements

• Accuracy:
  
  • Use a micrometer for precise diameter measurements.
  • Ensure the flying lead makes good contact to avoid inconsistent readings.
  • Repeat measurements to reduce random errors.
• Safety Considerations:
  
  • Avoid overheating by ensuring the circuit is set up correctly.
  • Handle the wire carefully to prevent injury.
• Limitations:
  
  • The wire may not have a perfectly circular cross-section, affecting area calculations.
  • Temperature changes may alter the wire’s resistance.
• Improvements:
  
  • Use a digital multimeter for more accurate readings.
  • Perform the experiment in a temperature-controlled environment.
  • Measure the diameter at more than three points for a better mean value.

Question 4

Potential divider (PAG)

Answer 4

Method and Calculations

• Set up the heat sensor:
  
  • Use a thermistor in a potential divider circuit (as shown in Figure 3).
  • Place the thermistor in a beaker of ice water, measure the initial temperature, and record the voltage across the thermistor.
• Record data:
  
  • Gradually heat the beaker, recording the temperature and voltage at regular intervals over a suitable range.
• Plot a graph:
  
  • Plot voltage (y-axis) against temperature (x-axis).

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Analysis (y = mx + c)

• Interpret the graph:
  
  • The graph should show that as temperature increases, the voltage decreases.
  • This is because the thermistor’s resistance decreases with increasing temperature, causing it to take a smaller share of the total potential difference.
  • The relationship is non-linear due to the thermistor’s exponential response to temperature.

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Accuracy, Safety, Limitations, and Improvements

• Accuracy:
  
  • Use a digital thermometer for precise temperature measurements.
  • Ensure the thermistor is fully submerged in the water for consistent readings.
  • Stir the water to maintain a uniform temperature.
• Safety Considerations:
  
  • Handle the hot water carefully to avoid burns.
  • Use a heat-resistant beaker and place it on a stable surface.
• Limitations:
  
  • The thermistor’s response may not be perfectly consistent due to manufacturing variations.
  • The non-linear relationship makes it harder to predict voltage changes at extreme temperatures.
• Improvements:
  
  • Use a data logger to automatically record voltage and temperature for greater precision.
  • Calibrate the thermistor using known temperature points for better accuracy.
  • Repeat the experiment with a different thermistor to check for consistency.

Question 5

Diffraction grating (PAG)

Answer 5

Method and Calculations

• Set up the experiment:
  
  • Pass monochromatic light through a diffraction grating to create a pattern of bright lines (maxima) on a dark background.
  • Identify the zero-order line (central maximum) and the first-order lines on either side.
• Measure the angle:
  
  • Use the small angle approximation to calculate the angle (θ) of the first-order line relative to the zero-order line, given the fringe width (x) and the distance to the screen (D).
• Calculate the wavelength:
  
  • Use the formula: nλ = d sinθ, where:
    
    • n = order of the maximum (e.g., 1 for first-order),
    • λ = wavelength of the light,
    • d = slit separation,
    • θ = angle between the maximum and the incident light.

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Analysis (y = mx + c)

• Interpret the pattern:
  
  • The bright lines are due to constructive interference, while the dark areas result from destructive interference.
  • For white light, the pattern splits into a spectrum from red (outside) to violet (inside) for each order, with the zero-order maximum remaining white.

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Accuracy, Safety, Limitations, and Improvements

• Accuracy:
  
  • Use a laser or high-quality monochromatic light source for clear, sharp fringes.
  • Measure the distance to the screen (D) and fringe width (x) carefully to minimize errors in calculating θ.
• Safety Considerations:
  
  • Avoid looking directly into the laser beam or bright light sources to protect your eyes.
  • Ensure the setup is stable to prevent the diffraction grating or screen from moving during the experiment.
• Limitations:
  
  • The small angle approximation may introduce errors for larger angles.
  • The diffraction grating may have imperfections, leading to less distinct fringes.
• Improvements:
  
  • Use a vernier scale or digital caliper to measure fringe widths more accurately.
  • Repeat the experiment with different slit separations (d) to verify consistency.
  • Use a spectrometer for more precise angle measurements.

Question 6

Plank constant (PAG)

Answer 6

Method and Calculations

• Set up the experiment:
  
  • Use monochromatic LEDs emitting a single wavelength of light.
  • Set the variable resistor to its maximum resistance to prevent current flow initially.
• Measure threshold voltage (V₀):
  
  • In a dark room, adjust the resistor until the LED just begins to light up.
  • Record the threshold voltage (V₀) and the wavelength (λ) of the emitted light.
• Repeat and average:
  
  • Repeat the experiment multiple times, averaging the results for V₀.
  • Perform the experiment for a range of LEDs with different wavelengths.
• Plot a graph:
  
  • Plot threshold voltage (V₀) against the inverse of the wavelength (1/λ).
  • The graph should be a straight line with the gradient = hc/e.
• Calculate Planck constant (h):
  
  • Use the gradient to calculate h = (gradient × e) / c.

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Analysis (y = mx + c)

• Interpret the graph:
  
  • The equation eV₀ = hc/λ corresponds to y = mx + c, where:
    
    • y = V₀,
    • x = 1/λ,
    • gradient (m) = hc/e,
    • y-intercept (c) = 0.
• Determine Planck constant (h):
  
  • Substitute the gradient into the equation h = (gradient × e) / c.

Accuracy, Safety, Limitations, and Improvements

• Systematic Errors:
  
  • Human error in identifying the exact voltage at which the LED begins to glow.
  • Use a black viewing tube in a darkened room for better accuracy.
  • A more accurate method: Plot a current vs. voltage graph and extrapolate to find the threshold voltage.
• Random Errors:
  
  • LEDs emit a narrow spectrum of light (∼60 nm width), not a single frequency.
  • The quoted wavelength is the central wavelength, but the lower end is emitted when the LED just glows, introducing error.
• Safety Considerations:
  
  • Do not stare directly at brightly lit LEDs, especially blue LEDs (close to UV).
  • Limit current to ≤ 50 mA (check LED ratings) to avoid damage.
  • Use a 330 Ω resistor to limit current.
  • Potentiometer hazard: Incorrect wiring can cause short circuits, leading to overheating and fire.
    
    • Turn off power immediately if burning is smelled.
  • Keep water away from electrical equipment.
• Improvements:
  
  • Use a spectrometer to measure the exact wavelength of light emitted by the LED.
  • Use a data logger to record voltage and current more accurately.
  • Repeat the experiment with a wider range of LEDs to improve the reliability of the graph.

Question 7

Internal resistance (PAG)

Answer 7

Method and Calculations

• Set up the circuit:
  
  • Set the variable resistor to its highest resistance.
  • Record the current (I) and potential difference (V) across the circuit.
• Repeat measurements:
  
  • Adjust the load resistance and repeat the measurements for multiple values.
  • Calculate the mean current and voltage for each resistance.
• Plot a graph:
  
  • Plot a V-I graph with mean data points and draw a line of best fit.
  • Ensure all variables, including temperature, are kept constant.
• Analyze results:
  
  • Determine the gradient (-r) and intercept (E) from the graph.
  • Use the equation V = E - Ir, where:
    
    • E = electromotive force (e.m.f.),
    • r = internal resistance.

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Analysis (y = mx + c)

• Interpret the graph:
  
  • The equation V = E - Ir corresponds to y = mx + c, where:
    
    • y = V,
    • x = I,
    • gradient (m) = -r,
    • y-intercept (c) = E.
• Determine internal resistance and e.m.f.:
  
  • The gradient gives the internal resistance (r).
  • The y-intercept gives the e.m.f. (E).

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Accuracy, Safety, Limitations, and Improvements

• Systematic Errors:
  
  • Close the switch briefly to take readings, preventing changes in the internal resistance of the battery.
• Random Errors:
  
  • Use fairly new cells to avoid variations in e.m.f. and internal resistance.
  • Wait for readings to stabilise before recording.
  • Take multiple repeats (at least 3) and calculate a mean to reduce errors.
• Safety Considerations:
  
  • Electrical components can get hot with prolonged use.
  • Switch off the power supply if burning is smelled.
  • Keep liquids away from equipment to avoid damage.
• Improvements:
  
  • Use a data logger to record current and voltage automatically for greater precision.
  • Perform the experiment in a temperature-controlled environment to minimize thermal effects.
  • Use a digital multimeter for more accurate measurements of current and voltage.

Question 8

Oscilloscope (PAG)

Answer 8

Cathode Ray Oscilloscope (CRO):

• Displays voltage over time from a signal generator, known as a trace.
• The type of trace depends on the source:
  
  • AC supply: Produces a trace that alternates between positive and negative patterns.
  • Sound waves: Converted into electrical signals by a microphone can also be displayed.

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Oscilloscope Screen:

• Divided into divisions:
  
  • Vertical axis: Represents volts.
  • Horizontal axis: Represents time.
• Volts per division and seconds per division are controlled by the gain and timebase dials, respectively.

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Wave Properties:

• Oscilloscope traces can be used to calculate:
  
  • Frequency: 1 ÷ period
  • Period: Measured using the timebase.

Question 9

Polarising filters for light (PAG)

Answer 9

Polarisation:

• Observed by shining unpolarised light through two polarising filters aligned vertically and rotating the second filter.
• Rotating the second filter reduces light intensity as its transmission axis deviates from vertical.

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Key Observations:

• At 45 degrees between transmission axes:
  
  • Intensity through the second filter is half that of the first.
• At right angles (90 degrees):
  
  • No light passes through.
• After 180-degree rotation:
  
  • Transmission axes realign, allowing all light through.

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Applications:

• Polaroid sunglasses: Use polarising filters to block partially polarised light, reducing glare.

Question 10

Speed of sound (PAG)

Answer 10

Method and Calculations

• Set up the experiment:
  
  • Place a hollow tube in water to create a closed-end pipe.
  • Note the frequency (f) of a tuning fork and hold it above the tube.
• Produce resonance:
  
  • Tap the tuning fork gently to produce sound waves that travel down the tube and reflect at the air/water surface.
  • Adjust the tube’s height until the sound resonates the loudest, indicating the lowest resonant frequency of the closed tube.
• Measure and calculate:
  
  • The tube’s length at resonance is a quarter of the sound wave’s wavelength (λ/4).
  • Use the frequency and wavelength to calculate the speed of sound in air using the equation:
    
    • v = fλ.

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Analysis

• Resonance condition:
  
  • For a closed pipe, the lowest resonant frequency occurs when the tube length is λ/4.
  • The relationship between the tube length (L) and wavelength (λ) is: L = λ/4.
• Calculate speed of sound:
  
  • Rearrange the equation to find λ = 4L.
  • Substitute λ and the known frequency (f) into v = fλ to calculate the speed of sound.

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Accuracy, Safety, Limitations, and Improvements

• Accuracy:
  
  • Ensure the tuning fork is struck gently to avoid overtones that could distort the resonance.
  • Measure the tube length carefully using a ruler with high precision.
  • Repeat the experiment to confirm the resonant length and calculate an average value.
• Safety Considerations:
  
  • Handle the tuning fork carefully to avoid injury or damage.
  • Ensure the tube is stable to prevent spills or accidents.
• Limitations:
  
  • The air/water surface may not be perfectly flat, affecting the reflection of sound waves.
  • Background noise can make it difficult to detect the loudest resonance.
• Improvements:
  
  • Use a microphone and oscilloscope to detect resonance more accurately.
  • Perform the experiment in a quiet environment to minimize interference.
  • Repeat with tuning forks of different frequencies to verify consistency.

Question 11

Semi circle light rays (PAG)

Answer 11

Method and Calculations

• Set up the experiment:
  
  • Place the glass block on paper and shine light from the ray box into the curved surface of the block.
• Find the critical angle:
  
  • Rotate either the ray box or the glass block until the refracted ray from the glass block makes an angle of 90° (grazes the surface).
  • Use a protractor to measure the angle of incidence (c) of the ray of light within the block; this is the critical angle.
• Calculate refractive index:
  
  • Use the formula: n = (sin c)^–1 to calculate the refractive index (n) of the glass block.

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Analysis

• Critical angle and refraction:
  
  • At the critical angle (c), the refracted ray travels along the boundary between the glass and air (angle of refraction = 90°).
  • The relationship between the refractive index (n) and the critical angle (c) is given by:
    
    • n = 1 / sin c.
• Interpretation:
  
  • A higher refractive index corresponds to a smaller critical angle, indicating greater bending of light.

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Accuracy, Safety, Limitations, and Improvements

• Accuracy:
  
  • Ensure the ray box produces a narrow, well-defined beam of light for precise measurements.
  • Use a protractor with high precision to measure the angle of incidence.
  • Repeat the experiment to confirm the critical angle and calculate an average value.
• Safety Considerations:
  
  • Handle the glass block carefully to avoid breakage or injury.
  • Avoid shining the light directly into eyes.
• Limitations:
  
  • The curved surface of the glass block may introduce errors in measuring the angle of incidence.
  • The ray box may produce a beam that is not perfectly collimated, affecting accuracy.
• Improvements:
  
  • Use a semicircular glass block to simplify the alignment of the incident and refracted rays.
  • Perform the experiment in a darkened room to improve visibility of the light beam.
  • Use a digital angle finder for more precise angle measurements.

Question 12

Center of mass (PAG)

Answer 12

1. Hang an object from a single point; the centre of mass will lie directly below that point.
2. Hang the object from two different points and draw a plumb line (a vertical line) from each point.
3. The intersection of these two lines is the centre of mass.

Question 13

Specific Heat Capacity (PAG)

Answer 13

Measuring Specific Heat Capacity

• Measure initial conditions:
  
  • Measure the mass (m) and initial temperature (T₁) of the substance.
• Heat the substance:
  
  • Use a heater to heat the substance, monitoring the change in temperature (ΔT).
  • Measure the current (I) and voltage (V) across the heater, and record the time (t) it is on.
• Calculate energy supplied:
  
  • Use the formula: E = V × I × t.
• Calculate specific heat capacity (c):
  
  • Use the formula: E = m × c × ΔT.
  • Rearrange to find: c = E / (m × ΔT).

Estimating Specific Heat Capacity Using Mixing Method

• Mix hot and cold substances:
  
  • Mix a hot substance (mass m₁, specific heat capacity c₁, initial temperature T₁) with a cold substance (mass m₂, specific heat capacity c₂, initial temperature T₂).
  • Measure the final temperature (T₀) once thermal equilibrium is reached.
• Calculate specific heat capacity:
  
  • Use the formula: m₁c₁(T₁ - T₀) = m₂c₂(T₀ - T₂).
  • Rearrange to find the unknown specific heat capacity (c₁ or c₂).

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Analysis

• Energy transfer:
  
  • In the heating method, the energy supplied by the heater is equal to the energy absorbed by the substance.
  • In the mixing method, the energy lost by the hot substance is equal to the energy gained by the cold substance (assuming no heat loss to the surroundings).
• Assumptions:
  
  • No heat is lost to the surroundings in the mixing method.
  • The heater is 100% efficient in the heating method.

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Accuracy, Safety, Limitations, and Improvements

• Accuracy:
  
  • Use a thermometer with high precision to measure temperature changes.
  • Ensure the heater is fully submerged and the substance is well-insulated to minimize heat loss.
  • Repeat measurements to reduce random errors.
• Safety Considerations:
  
  • Handle hot substances carefully to avoid burns.
  • Ensure electrical equipment (e.g., heater) is properly insulated to prevent electric shocks.
• Limitations:
  
  • Heat loss to the surroundings can affect results in both methods.
  • The mixing method assumes no heat loss, which is not always realistic.
• Improvements:
  
  • Use a calorimeter to minimize heat loss in the mixing method.
  • Perform the experiment in a temperature-controlled environment.
  • Use a data logger to monitor temperature changes continuously.

Question 14

Specific Latent Heat (PAG)

Answer 14

Method and Calculations

Measuring Specific Latent Heat of Fusion

• Set up the experiment:
  
  • Use a heating coil in one funnel of ice.
  • Connect the coil to an ammeter and voltmeter.
• Heat the ice:
  
  • Turn the heater on for three minutes and measure the current (I) and voltage (V).
  • Calculate the energy transferred using W = VIt.
• Measure melted ice:
  
  • Use a second unheated funnel to measure the mass of ice melted at room temperature.
  • Subtract the unheated mass from the heated mass to find the mass of ice melted due to the heater (m).
• Calculate latent heat of fusion:
  
  • Use the formula: E = mL, where L is the specific latent heat of fusion.
  • Rearrange to find: L = E/m.

Measuring Specific Latent Heat of Vaporisation

• Set up the experiment:
  
  • Place a heating coil in a beaker of water, and insulate the outside of the beaker.
  • Connect the coil to an ammeter and voltmeter.
• Heat the water:
  
  • Start heating the water and monitor the mass of water as it boils, using a mass balance.
  • Measure the voltage (V) and current (I) across the heating coil.
  • Once the mass decreases by about 15 g, stop the timer.
• Calculate energy transferred:
  
  • Use the formula: W = VIt.
• Calculate latent heat of vaporisation:
  
  • Use the formula: L = E/m, where E is the energy transferred and m is the mass lost.

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Analysis

• Energy transfer:
  
  • In both experiments, the energy supplied by the heater is used to change the state of the substance (ice to water or water to steam) without changing its temperature.
• Key equations:
  
  • For fusion: E = mL_f.
  • For vaporisation: E = mL_v.

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Accuracy, Safety, Limitations, and Improvements

• Accuracy:
  
  • Use a high-precision mass balance to measure the mass of ice or water.
  • Ensure the heating coil is fully submerged and the system is well-insulated to minimize heat loss.
  • Repeat measurements to reduce random errors.
• Safety Considerations:
  
  • Handle hot water and steam carefully to avoid burns.
  • Ensure electrical equipment (e.g., heater) is properly insulated to prevent electric shocks.
• Limitations:
  
  • Heat loss to the surroundings can affect results.
  • The mass of ice melted at room temperature may vary due to environmental factors.
• Improvements:
  
  • Use a calorimeter to minimize heat loss.
  • Perform the experiment in a temperature-controlled environment.
  • Use a data logger to monitor temperature and mass changes continuously.

Question 15

Boyle’s Law (PAG)

Answer 15

Method and Calculations

• Set up the apparatus:
  
  • Use a sealed tube containing air and oil, a Bourdon gauge for pressure measurement, and a tyre pump to vary pressure.
• Measure pressure and volume:
  
  • Increase pressure by pumping air into the system.
  • Measure pressure (p) with the Bourdon gauge.
  • Calculate volume (V) by multiplying the length of the air-containing part of the tube by the tube’s cross-sectional area (A = πr²).
• Record data:
  
  • Gradually increase pressure at set intervals and wait for temperature to stabilize before recording readings.
  • Multiply pressure and volume at each point; they should give the same value if Boyle’s Law is valid.
• Repeat and average:
  
  • Repeat the experiment and calculate the mean for each reading.

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Analysis

• Boyle’s Law verification:
  
  • Boyle’s Law states that pV = constant for a fixed mass of gas at constant temperature.
  • The product of pressure (p) and volume (V) should remain constant if the law holds.
• Graph plotting:
  
  • Plot pressure (p) against volume (V).
  • The graph should show a hyperbolic curve, confirming the inverse proportionality between pressure and volume.
  • Alternatively, plot p against 1/V to obtain a straight line passing through the origin.

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Accuracy, Safety, Limitations, and Improvements

• Accuracy:
  
  • Ensure the temperature remains constant throughout the experiment.
  • Use a high-precision Bourdon gauge for accurate pressure measurements.
  • Measure the length of the air column carefully using a ruler with high resolution.
• Safety Considerations:
  
  • Avoid over-pressurising the system to prevent the tube or gauge from bursting.
  • Handle the tyre pump carefully to avoid injury.
• Limitations:
  
  • The oil in the tube may introduce errors if it affects the air volume or pressure measurements.
  • The assumption of constant temperature may not hold if the experiment is conducted too quickly.
• Improvements:
  
  • Use a digital pressure sensor for more accurate and consistent readings.
  • Perform the experiment in a temperature-controlled environment.
  • Repeat the experiment multiple times to reduce random errors.

Question 16

Absolute Zero (PAG)

Answer 16

Method and Calculations

• Set up the apparatus:
  
  • Submerge a stoppered flask filled with air into a beaker of water.
  • Connect the stopper to a Bourdon gauge with tubing (ensure the tubing’s volume is much smaller than the flask’s volume).
• Record initial conditions:
  
  • Record the temperature of the water and the pressure on the Bourdon gauge.
• Heat the water:
  
  • Insert an electric heater, heat the water for a few minutes, then remove it.
  • Stir the water to ensure a uniform temperature and allow time for heat transfer to the air inside the flask.
  • Record the pressure and temperature.
• Repeat and average:
  
  • Repeat several times, heating the water incrementally until it starts to boil.
  • Repeat the entire experiment twice more with fresh cool water.

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Analysis

• Pressure Law verification:
  
  • The Pressure Law states that p/T = constant for a fixed mass of gas at constant volume.
  • Multiplying pressure (p) and temperature (T) together should yield a constant if the law holds.
• Graph plotting:
  
  • Plot pressure (p) against temperature (T).
  • Draw a line of best fit and extrapolate it to the x-axis to estimate the value of absolute zero.
  • The graph should be a straight line passing through the origin when temperature is in Kelvin.

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Accuracy, Safety, Limitations, and Improvements

• Accuracy:
  
  • Ensure the temperature is uniform by stirring the water thoroughly.
  • Use a high-precision thermometer and Bourdon gauge for accurate measurements.
  • Repeat the experiment multiple times to reduce random errors.
• Safety Considerations:
  
  • Handle the electric heater carefully to avoid burns or electric shocks.
  • Avoid overheating the water to prevent the flask or tubing from cracking.
• Limitations:
  
  • The Bourdon gauge may have a limited range, affecting measurements at high pressures.
  • Heat loss to the surroundings may affect the accuracy of temperature measurements.
• Improvements:
  
  • Use a digital pressure sensor and temperature probe for more accurate and consistent readings.
  • Perform the experiment in a temperature-controlled environment.
  • Insulate the beaker to minimize heat loss to the surroundings.

Question 17

Circular Motion (PAG)

Answer 17

Method and Calculations

• Set up the apparatus:
  
  • Attach a bung to a string threaded through a plastic tube.
  • Weigh the washers used to anchor the free end of the string.
  • Measure the radius (r), which is the distance from the bung to the reference mark.
• Spin the bung:
  
  • Rotate the bung in a horizontal circle while keeping the reference mark level with the tube’s top.
  • Adjust the speed to prevent the mark from moving.
• Measure time period:
  
  • Record the time (T) for one complete circle or multiple circles for greater accuracy.
• Calculate angular speed:
  
  • Use the formula: ⍵ = 2π/T.
• Calculate centripetal force:
  
  • Use the formula: F = m⍵²r, where m is the mass of the bung.

===

Analysis

• Observation:
  
  • Repeat the experiment for different values of r.
  • As r increases, the time period (T) lengthens, but the centripetal force remains constant, equal to the weight of the washers (W = mg).
• Key relationships:
  
  • The centripetal force is provided by the tension in the string, which is balanced by the weight of the washers.
  • The relationship between radius (r), angular speed (⍵), and centripetal force (F) is given by F = m⍵²r.

===

Accuracy, Safety, Limitations, and Improvements

• Accuracy:
  
  • Ensure the reference mark remains level with the tube’s top to maintain a constant radius.
  • Use a stopwatch to measure the time period accurately.
  • Repeat measurements to reduce random errors.
• Safety Considerations:
  
  • Ensure the string is securely attached to the bung and tube to prevent it from slipping or breaking.
  • Spin the bung carefully to avoid hitting nearby objects or people.
• Limitations:
  
  • Air resistance may affect the motion of the bung, especially at high speeds.
  • The string may stretch slightly, introducing errors in the measurement of r.
• Improvements:
  
  • Use a light gate or motion sensor to measure the time period more accurately.
  • Perform the experiment in a controlled environment to minimize air resistance.
  • Use a stiffer string to reduce stretching.

Question 18

SHM (PAG)

Answer 18

Method and Calculations

Using Sensors and a Data Logger

• Set up the experiment:
  
  • Use a position sensor connected to a data logger to record the displacement-time graph for a mass-spring system oscillating in SHM.
• Analyze the graph:
  
  • Measure the amplitude (A) and time period (T) from the graph.
  • Calculate the frequency (f) using f = 1/T.
• Observe energy loss:
  
  • As oscillations progress, the amplitude decreases due to energy loss, but the time period and frequency remain constant.

Without Sensors and a Data Logger

• Set up the pendulum:
  
  • Use a pendulum setup with a ruler, protractor, and stopwatch.
  • Measure the length of the string, mass weight, and initial displacement angle (<10°) for accurate results.
• Record oscillations:
  
  • Record the time period (T) for several oscillations and calculate the frequency (f) using f = 1/T.
• Investigate variables:
  
  • Changing the string length affects T, but mass and angle have no effect on T.

===

Analysis

• SHM characteristics:
  
  • In SHM, the time period (T) and frequency (f) are independent of amplitude and mass (for a pendulum).
  • The displacement-time graph for SHM is sinusoidal, showing the relationship between displacement and time.
• Energy loss:
  
  • In real systems, energy is lost due to air resistance or friction, causing the amplitude to decrease over time.

===

Accuracy, Safety, Limitations, and Improvements

• Accuracy:
  
  • For the mass-spring system, ensure the position sensor is calibrated correctly.
  • For the pendulum, measure the string length and angle carefully using a ruler and protractor.
  • Use a stopwatch with high precision to measure time periods.
• Safety Considerations:
  
  • Ensure the pendulum setup is stable to prevent the mass from swinging into nearby objects or people.
  • Handle the mass-spring system carefully to avoid injury from the spring or mass.
• Limitations:
  
  • Air resistance and friction can affect the accuracy of results, especially in the mass-spring system.
  • Manual measurements (e.g., stopwatch) may introduce human error.
• Improvements:
  
  • Use a light gate or motion sensor to measure time periods more accurately for the pendulum.
  • Perform the experiment in a vacuum or controlled environment to minimize air resistance.
  • Repeat measurements multiple times to reduce random errors.

Question 19

Capacitors in Series and Parallel (PAG)

Answer 19

Method and Calculations

Capacitors in Series

• Set up the circuit:
  
  • Connect three identical capacitors in series.
  • Set the variable resistor to a high resistance value and record it.
• Charge the capacitors:
  
  • Close the switch to start charging the capacitors.
  • Record the initial current in the circuit.
  • Use a data logger connected to a voltmeter to record the potential difference across the capacitors over time.
  • Adjust the variable resistor to maintain a constant current as much as possible.
• Monitor the current:
  
  • Once the capacitors are fully charged (current drops to zero), open the switch.

Capacitors in Parallel

• Set up the circuit:
  
  • Connect another three identical capacitors in parallel.
  • Repeat the same steps as for the series circuit, ensuring the variable resistor starts at the same resistance value.

===

Analysis

• Plot a charge vs. potential difference graph for each circuit, using ΔQ = IΔt to calculate the charge stored by the capacitors at each time reading.
• Graph interpretation:
  
  • The charge vs. potential difference graph should be a straight line through the origin, with the gradient representing the total capacitance of the circuit.
• Compare results:
  
  • Compare the experimental total capacitance (from the gradient) with the theoretical values for capacitors in series and parallel:
    
    • Series: 1/C_total = 1/C₁ + 1/C₂ + 1/C₃.
    • Parallel: C_total = C₁ + C₂ + C₃.

• Accuracy:
  
  • Use a high-precision voltmeter and ammeter for accurate measurements.
  • Ensure the variable resistor is adjusted smoothly to maintain a constant current.
  • Repeat the experiment to reduce random errors.
• Safety Considerations:
  
  • Handle the capacitors carefully to avoid short circuits or electric shocks.
  • Ensure the circuit is properly insulated and connections are secure.
• Limitations:
  
  • Maintaining a constant current may be difficult as the capacitors approach full charge.
  • The capacitors may have slight variations in capacitance, affecting results.
• Improvements:
  
  • Use a digital data logger for more precise and automated recordings.
  • Perform the experiment in a controlled environment to minimize external interference.
  • Use capacitors with known and identical capacitance values for better comparison.

Question 20

Investigating Charging and Discharging Capacitors (PAG)

Answer 20

Method and Calculations

Investigating Charging a Capacitor

• Set up the circuit:
  
  • Use a fixed resistor to slow down the charging process.
  • Connect a voltmeter and ammeter to measure potential difference and current, respectively.
• Charge the capacitor:
  
  • Close the switch to begin charging the capacitor.
  • Use a data logger to record potential difference and current over time.
  • Observe the current: When it drops to zero, the capacitor is fully charged.
• Plot graphs:
  
  • Plot current, potential difference, and charge (ΔQ = IΔt) against time.

Investigating Discharging a Capacitor

• Discharge the capacitor:
  
  • Open the switch and disconnect the power supply.
  • Close the switch to allow the capacitor to discharge.
  • Use the data logger to record potential difference and current over time.
  • Observe the current: When it reaches zero, the capacitor is fully discharged.
• Plot graphs:
  
  • Plot current, potential difference, and charge (ΔQ = IΔt) against time.

===

Analysis

Charging a Capacitor

• Initial conditions:
  
  • At the start, the current is high because the potential difference across the capacitor is zero.
• During charging:
  
  • As the capacitor charges, the potential difference across it increases, causing the current to decrease.
  • The charge (Q) on the capacitor is directly proportional to the potential difference (V) across it (Q = CV).

Discharging a Capacitor

• Initial conditions:
  
  • At the start of discharging, the current is high.
• During discharging:
  
  • As charge leaves the plates, the potential difference decreases, and the current reduces.
  • The charge (Q) and potential difference (V) decrease exponentially over time.

===

Accuracy, Safety, Limitations, and Improvements

• Accuracy:
  
  • Use a high-precision voltmeter and ammeter for accurate measurements.
  • Ensure the data logger records data at regular intervals for consistent results.
  • Repeat the experiment to reduce random errors.
• Safety Considerations:
  
  • Handle the capacitor carefully to avoid electric shocks, especially when fully charged.
  • Ensure the circuit is properly insulated and connections are secure.
• Limitations:
  
  • The fixed resistor may heat up during the experiment, affecting its resistance.
  • The capacitor may have a slight leakage current, affecting discharge measurements.
• Improvements:
  
  • Use a digital data logger for more precise and automated recordings.
  • Perform the experiment in a controlled environment to minimize external interference.
  • Use capacitors with low leakage for more accurate results.

Question 21

Magnetic Flux Density (PAG)

Answer 21

Method and Calculations

• Set up the experiment:
  
  • Position a square hoop of metal wire so that the top of the hoop (length L) is perpendicular to the magnetic field.
  • Connect the d.c. power supply to a variable resistor to control the current.
  • Place the setup on a digital balance and zero it when there is no current.
• Measure force and current:
  
  • Turn on the d.c. power supply and ensure the mass reading is positive (if negative, swap the crocodile clips).
  • Record the mass and current for different values of current using the variable resistor.
  • Repeat for a large range of currents, taking three readings for each current to improve accuracy.
• Convert mass to force:
  
  • Use F = mg to convert mass readings to force.
• Plot a graph:
  
  • Plot force (F) against current (I) and draw a line of best fit.

===

Analysis

• Graph interpretation:
  
  • The graph should pass through the origin, showing that force is proportional to current.
  • The gradient of the line is equal to B / L, where:
    
    • B = magnetic flux density,
    • L = length of the wire in the magnetic field.
• Calculate magnetic flux density (B):
  
  • Use the formula: B = gradient × L.

===

Accuracy, Safety, Limitations, and Improvements

• Accuracy:
  
  • Ensure the wire length (L) is measured accurately using a ruler with high precision.
  • Use a high-precision digital balance to measure mass.
  • Repeat measurements to reduce random errors.
• Safety Considerations:
  
  • Handle the d.c. power supply carefully to avoid short circuits or electric shocks.
  • Ensure the setup is stable to prevent the wire or balance from moving during the experiment.
• Limitations:
  
  • The magnetic field may not be perfectly uniform, affecting results.
  • The wire may heat up due to high currents, altering its resistance and affecting measurements.
• Improvements:
  
  • Use a stronger and more uniform magnetic field for more consistent results.
  • Perform the experiment in a temperature-controlled environment to minimize thermal effects.
  • Use a data logger to automate current and force measurements for greater precision.

Question 22

Magnetic Flux (PAG)

Answer 22

Method and Calculations

1. Set up the magnets:
   
   • Place two bar magnets a small distance apart with opposite poles facing each other.
   • Ensure they are far enough apart not to snap together but close enough to create a uniform magnetic field.
2. Prepare the search coil:
   
   • Use a search coil with a known number of turns (N) and area (A).
   • Connect the coil to a data recorder set to measure the induced e.m.f. with a very small time interval between readings.
3. Position the coil:
   
   • Place the search coil in the middle of the magnetic field, ensuring the coil’s area is parallel to the surface of the magnets.
   • Start the data recorder.
4. Induce e.m.f.:
   
   • While keeping the coil in the same orientation, move the coil out of the magnetic field immediately.
   • As the coil moves out, the e.m.f. is induced due to the changing magnetic flux linkage, going from maximum (NΦ) to zero.
5. Plot and calculate:
   
   • Use the data from the recorder to plot a graph of induced e.m.f. against time.
   • Estimate the area under the graph to calculate the change in flux linkage using Faraday’s Law.
   • The change in flux linkage equals the flux linkage in the uniform magnetic field (since the final flux linkage is zero).
   • Calculate Φ using: Φ = (change in flux linkage) / N.
6. Repeat:
   
   • Repeat the experiment multiple times and calculate the mean value of Φ to improve precision.

===

Analysis

• Faraday’s Law:
  
  • The induced e.m.f. is proportional to the rate of change of magnetic flux linkage.
  • The area under the e.m.f. vs. time graph represents the change in flux linkage.
• Flux linkage calculation:
  
  • Flux linkage (NΦ) is the product of the number of turns (N) and the magnetic flux (Φ).
  • Use Φ = (change in flux linkage) / N to find the magnetic flux in the uniform field.

===

Accuracy, Safety, Limitations, and Improvements

• Accuracy:
  
  • Ensure the search coil is moved out of the magnetic field quickly and smoothly to avoid inconsistent readings.
  • Use a high-precision data recorder to measure the induced e.m.f. accurately.
  • Repeat the experiment multiple times to reduce random errors.
• Safety Considerations:
  
  • Handle the magnets carefully to avoid pinching or injury.
  • Ensure the setup is stable to prevent the magnets or coil from moving unexpectedly.
• Limitations:
  
  • The magnetic field may not be perfectly uniform, affecting results.
  • The search coil may have slight variations in its area or number of turns.
• Improvements:
  
  • Use a stronger and more uniform magnetic field for more consistent results.
  • Perform the experiment in a controlled environment to minimize external interference.
  • Use a calibrated search coil with precise dimensions and turns.

Question 23

Transformers (PAG)

Answer 23

Method and Calculations

Relationship Between Turns and Voltage

• Set up the transformer:
  
  • Use two cores with wire wrapped around them to form primary and secondary coils.
  • Start with a turns ratio of 1:2 (e.g., 5 turns in the primary coil and 10 in the secondary coil).
• Measure voltages:
  
  • Turn on the a.c. supply at a low voltage for safety.
  • Measure the voltage across each coil while keeping the primary voltage constant.
• Repeat for other ratios:
  
  • Repeat the experiment for other turns ratios, such as 1:1 and 2:1.
• Calculate ratios:
  
  • Calculate n₁/n₂ (turns ratio) and V₁/V₂ (voltage ratio).
  • The ratios should be equal, confirming V₁/V₂ = n₁/n₂.

Relationship Between Current and Voltage

• Modify the setup:
  
  • Add a variable resistor and ammeters to the transformer setup.
• Record current and voltage:
  
  • Record the current (I₁) and voltage (V₁) across the primary coil, and current (I₂) and voltage (V₂) across the secondary coil.
  • Adjust the variable resistor to change the input current, recording the corresponding values for both coils.
• Confirm power conservation:
  
  • For each current, confirm P = V₁I₁ = V₂I₂ (power remains constant, neglecting losses).

===

Analysis

• Turns and voltage relationship:
  
  • The voltage ratio (V₁/V₂) is equal to the turns ratio (n₁/n₂), confirming the transformer equation: V₁/V₂ = n₁/n₂.
• Current and voltage relationship:
  
  • The power in the primary coil (V₁I₁) should equal the power in the secondary coil (V₂I₂), assuming no energy losses.
  • This confirms the principle of energy conservation in an ideal transformer.

===

Accuracy, Safety, Limitations, and Improvements

• Accuracy:
  
  • Use a high-precision voltmeter and ammeter for accurate measurements.
  • Ensure the a.c. supply is stable and set to a low voltage for safety and consistency.
  • Repeat measurements to reduce random errors.
• Safety Considerations:
  
  • Handle the a.c. supply carefully to avoid electric shocks.
  • Ensure the setup is properly insulated and connections are secure.
• Limitations:
  
  • Real transformers have energy losses (e.g., heat, eddy currents), which may cause slight deviations from ideal results.
  • The magnetic field may not be perfectly uniform, affecting the transformer’s efficiency.
• Improvements:
  
  • Use a digital data logger to automate voltage and current measurements for greater precision.
  • Perform the experiment in a controlled environment to minimize external interference.
  • Use laminated cores to reduce eddy current losses.

Question 24

Terminal Velocity in Fluids

Answer 24

Method and Calculations

• Set up the experiment:
  
  • Wrap elastic bands or mark intervals on a tube of viscous liquid using a ruler.
  • Release a ball bearing from rest above the liquid.
• Record data:
  
  • Use a stopwatch to record the time it takes for the ball bearing to reach each mark.
  • Calculate the average speed between intervals using speed = distance / time.
• Repeat and average:
  
  • Repeat the experiment multiple times for a range of readings to improve accuracy.

===

Analysis

• Terminal velocity:
  
  • When the ball bearing reaches terminal velocity, the distance between intervals becomes constant.
• Plot a velocity-time graph:
  
  • The graph should show the velocity increasing initially and then plateauing (zero gradient) at terminal velocity.

===

Accuracy, Safety, Limitations, and Improvements

Systematic Errors:
- Use a more viscous or denser fluid to slow the ball bearing and make terminal velocity easier to observe.
- Use a taller tube to allow the ball bearing to travel longer at terminal velocity.
- Use larger intervals to reduce percentage uncertainty in distance and time measurements.

Random Errors:
- Repeat the experiment at least four times to reduce random errors.
- Use ticker tape or a motion sensor instead of a stopwatch for more precise time measurements.

Safety Considerations:
- Handle the viscous liquid carefully to avoid spills or contamination.
- Ensure the tube is stable and securely placed to prevent accidents.

Limitations:
- The viscosity of the liquid may change with temperature, affecting results.
- Human reaction time may introduce errors when using a stopwatch.

Improvements:
- Use a digital motion sensor to track the ball bearing’s position and velocity automatically.
- Perform the experiment in a temperature-controlled environment to minimize changes in viscosity.
- Use a larger ball bearing to reduce the effect of random fluctuations in motion.

Question 25

Ripple Tank (PAG)

Answer 25

Apparatus Setup:

• Motorized bar produces plane waves (straight wavefronts)
• Small dipper produces circular waves
• Overhead light source projects wave patterns onto screen below
• Glass sheet (for refraction experiments)
• Barriers (for reflection/diffraction studies)

===

Key Wave Properties Demonstrated:

1. Wave Visualization:
   
   • Bright bands on screen represent wave crests
   • Enables direct measurement of wavelength (λ)
   • Clear observation of wavefronts and their behavior
2. Wave Phenomena:
   
   • Reflection:
     
     • Use plane/curved surfaces
     • Measure angles of incidence/reflection relative to normal
     • Verify law of reflection (θi = θr)
   • Refraction:
     
     • Glass sheet creates shallow region (changes wave speed)
     • Observe wavelength change at boundary
     • Wavefronts closer together = slower speed (and vice versa)
   • Diffraction:
     
     • Observe wave bending around barriers
     • Most noticeable when gap width ≈ wavelength
   • Interference:
     
     • Two dippers produce overlapping circular waves
     • Observe constructive/destructive interference patterns

===

Experimental Control:
- Adjust motor frequency to change wavelength
- Vary bar angle to change wave direction
- Modify water depth to alter wave speed

===

Practical Considerations:
- Ensure water depth is uniform for baseline measurements
- Use stroboscopic lighting to ‘freeze’ wave patterns
- Calibrate measurements using known barrier spacing

===

Key Relationships Demonstrated:
- v = fλ (wave equation)
- n = c/v (refractive index)
- sinθi/sinθr = n (Snell’s Law)

Question 26

Alpha, Beta & Gamma Radiation (PAG)

Answer 26

Safety Protocols

• Storage: Keep radioactive sources in a lead-lined box when not in use
• Handling: Use long-handled tongs (minimum 30cm length)
• Positioning:
  
  • Maintain >50cm distance from active sources
  • Never point sources toward people
• PPE: Wear lab coat, gloves, and safety goggles

===

Equipment Setup

1. Geiger-Müller tube connected to counter
2. Radioactive sources (α, β, γ) - clearly labeled
3. Test materials (paper, aluminum, lead sheets of varying thicknesses)
4. Measuring ruler for precise source-detector distances

===

Experimental Procedure

A. Baseline Measurements
1. Measure background radiation:
- 3 x 30-second readings (no source present)
- Calculate mean background count rate (counts/sec)

2. Measure source radiation:
   
   • Position source 5cm from GM tube
   • Take 3 x 30-second readings
   • Calculate net count rate (source rate - background)

B. Penetration Tests
1. Material Testing:
- Insert test material between source and detector
- Record count rate changes for:
- Paper (α test)
- 2mm aluminum (β test)
- 5mm lead (γ test)

2. Quantitative Analysis:
   
   • For γ radiation:
     
     • Measure count rate through lead sheets (0.5mm to 10mm thickness)
     • Plot absorption curve (count rate vs thickness)

C. Distance Investigation
1. Vary source-detector distance (5-50cm)
2. Verify inverse square law for γ radiation

===

Data Analysis

• Absorption Calculation:
  % absorption = 100 × (1 - (net count with material/net count without))
• Half-Value Thickness:
  Determine thickness required to halve radiation intensity

===

Common Experimental Errors

1. Not accounting for dead time in GM tube at high count rates
2. Inconsistent source-detector alignment
3. Neglecting to subtract background from all measurements