Creating Models Flashcards

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0
Q

What can make an atom unstable?

A

Having too many neutrons
Having too few neutrons
Having too much energy

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1
Q

What is a model?

A

A set of assumptions which simplifies a problem.

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2
Q

How do unstable atoms become stable?

A

By emitting particles and/or energy

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3
Q

What is radioactive decay?

A

The release of particles and/or energy by a radioactive atom until it is stable

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4
Q

What type of process is radioactive decay?

A

A random process

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5
Q

What is the activity of a sample of radioactive atoms?

A

The number of unstable atoms that decay each second.

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6
Q

What is the activity of a sample of radioactive atoms proportional to?

A

The number of atoms in that sample

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7
Q

What is the differential equation for the rate at which a sample of radioactive atoms decays?

A

dN/dT= -λN

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8
Q

What is does the decay constant define?

A

The probability of a given nucleus decaying over one second

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9
Q

What the units of the decay constant?

A

s⁻¹

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10
Q

If the decay constant increases, does the rate of decay increase or decrease?

A

The rate of decay increases - more particles decay per second

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11
Q

Activity is measured in…

A

Becquerels (Bq)

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12
Q

What is one becquerel equivalent to?

A

1 atom decaying over 1 second

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13
Q

If a radioactive sample of atoms is left to decay, how many atoms will there be at time t, given that there were initially N₀ atoms in the sample?

A

N₀e^(-λt), where lambda is the decay constant of the sample.

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14
Q

What is the half life of an isotope?

A

The average time it takes half a sample of that isotope to decay.

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15
Q

What is the equation for the half-life of an isotope?

A

T = ln2 / λ

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16
Q

What is capacitance defined as?

A

The amount of charge stored per unit volt

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17
Q

Why are capacitors used in flash photography?

A

To provide a short burst of high current, which creates a brief intense flash of light

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18
Q

Why are variable capacitors used in defibrillators?

A

To allow the user to alter the amount of charge stored on the plates, further altering the magnitude of the current applied to the patient

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19
Q

Why would capacitors be used in a desktop computer?

A

To prevent data being lost when the power is cut - they act as back-up supplies, allowing the computer to store the data before shutting down

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20
Q

What is the equation for the amount of energy a capacitor can store?

A

E = QV/2

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21
Q

How are capacitors able to store energy? I.e. Where does the energy initially come from?

A

Capacitors are able to store energy because work is done moving energy from one plate to another.

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22
Q

Describe how a capacitor is charged.

A

Electrons flow from the circuit onto the plate connected to the negative terminal of the battery.
This build-up of charge pushes electrons off the opposite plate, making it positive. The charge builds up on the plates until the potential difference across the plates equals the p.d. across the source.

23
Q

Why does a capacitor stop charging once its p.d. equals that of the source?

A

Because the potential difference across the capacitor opposes that of the source - the net potential difference for the circuit is equal to zero.

24
Q

What does the discharge time of a capacitor circuit depend on?

A

Capacitance - how much charge there is to release

Resistance - how quickly that charge can flow from the capacitor around the circuit

25
Q

What is the equation for the rate of charge for a capacitor?

A

dQ/dt = Q/RC

26
Q

What is the equation for the rate of discharge for a capacitor?

A

dQ/dt = -Q/RC

27
Q

What is the charge on a discharging capacitor at time t, where Q₀ is the charge on the capacitor at t = 0?

A

Q = Q₀e^(-t/RC)

28
Q

What is the equation for the voltage across a charging capacitor?

A

V₀ = Vs - Vs e^(-t/RC)

29
Q

What is the time constant equivalent to when a capacitor is charging?

A

The time when the capacitor is 63% charged.

30
Q

What is the time constant equivalent to when a capacitor is discharging?

A

The time when the charge on the capacitor is 37% the total charge.

31
Q

What is simple harmonic motion?

A

Am oscillation in which the acceleration of an object is directly proportional to its displacement from a midpoint, and is directed towards that midpoint.

32
Q

What types of energy does a simple harmonic oscillator have?

A

Potential energy and kinetic energy.

33
Q

What is the mechanical energy of a system equivalent to?

A

The kinetic energy plus the potential energy of that system.

34
Q

What is the maximum velocity of a SHM pendulum?

A

2πfA
A = Amplitude of the oscillations
f = oscillation frequency

35
Q

What is the maximum acceleration of an SHM pendulum?

A

-(2πf)²A

36
Q

Does amplitude affect frequency?

A

No.

37
Q

Why can a SHM clock still keep time, even if it’s swing becomes significantly smaller?

A

Their time period does not depend on amplitude, therefore they will continue to keep time regularly.

38
Q

What is the displacement of a SHM pendulum released at time t from the peak of its swing?

A

ACos(2πft)

39
Q

What is the displacement of a SHM pendulum at time t, given that the timer was started as the oscillator passed its midpoint?

A

ASin(2πft)

40
Q

What is the relationship between angular velocity and frequency?

A

Omega = 2πf

41
Q

What is the time period of a simple harmonic oscillator?

A

T = 2πROOT(m/k)

Where k is the Young modulus of the spring

42
Q

What is the potential energy of a spring extended distance x from its rest position?

A

(kx²)/2

43
Q

What is the acceleration of a simple harmonic oscillator at extension x?

A

-(k/m)x

44
Q

What is the time period of a pendulum?

A

T = 2πROOT(l/g)

Where l is the length of hyena pendulum’s string.

45
Q

What is a free vibration?

A

A free vibration is a vibration which transfers no energy to or from its surroundings.

46
Q

Define a forced vibration.

A

A forced vibration is a vibration created by a periodic external force.

47
Q

What is the natural frequency of a system?

A

The frequency a system oscillates at when not subjected to a periodic external force.

48
Q

When does resonance occur?

A

When the driving frequency of a vibration is equivalent to the natural frequency of the system.

49
Q

What is resonance?

A

When a system consistently receives energy from a force whose driving frequency is equal to the natural frequency of that system.

50
Q

How does damping prevent resonance occurring?

A

By absorbing energy from the system - the system loses energy to its surroundings.

51
Q

What is critical damping of a system?

A

When the amount of damping applied to system reduces the amplitude of that system’s vibrations in the least possible time.

52
Q

What is the term for when the actual damping is greater than the critical damping? Does this amount of damping take more or less time to reduce the amplitude of a system’s vibrations?

A

Overdamping. It takes more time.

53
Q

What is the form of a resonance peak of a lightly damped system?

A

Sharp.

54
Q

What is the form of a heavily damped system’s resonance peak?

A

Flat.