TURNING POINTS: QUESTIONS

Question 1

Bertozzi’s experiment was designed to test the relationship between the kinetic energy of an electron and its speed as predicted by the theory of special relativity.

Describe Bertozzi’s experiment.

Your answer should include:

• a diagram of the experimental arrangement
• details of how the kinetic energy and the speed were measured.

(6)

Answer 1

lvl 5-6: Candidate will draw a useful diagram, and give a coherent well-structured attempt at explaining how energy and velocity are measured with some equations and the use made of the measurements

The following statements could be present:

• useful diagram
• pulses of electrons produced in an accelerator
• electron beam detected as it passes A and B
• time of flight measured with oscilloscope
• velocity = AB / time
• each pulse of electrons raises temperature of aluminium plate
• temperature rise of plate measured (process of finding energy from heat is calorimetry)
• energy landing on plate mcΔθ
• energy of electron = mcΔθ/n (n = number of electrons hitting the plate)
• e and v measured for different electron energies
• compared with prediction from relativity.

Question 2

Label a transmission electron microscope

Answer 2

• condenser lens forms a wide parallel beam of electrons
• objective lens magnifies and forms an image of the sample
• projector lens magnifies and focuses the image (projecting it)

Question 3

A typical TEM can accelerate electrons to very high speeds and form high resolution images.

Explain:

• the process of image formation, and
• the factors that affect the quality of, and the level of detail in, the image.

(6)

Answer 3

6 marks: At least six of the likely statements will be covered to a good standard including at least three from image formation and at least three from quality and detail.

Process of Image formation:

• Electrons through the middle of the lenses are undeviated
• Electrons on the edges are deflected by magnetic fields toward the axis of the TEM
• The condenser lens deflects the electrons into a wide parallel beam incident uniformly on the sample.
• The objective lens then forms an image of the sample.
• The projector lens then casts a second image onto the fluorescent screen.

The screen’s atoms are energised and then emit photons so we can see the image

Factors affecting the quality and level of detail:

• Wavelength depends on speed of the electrons
• Lower the wavelength gives greater the detail.
• Emitted electrons come from a heated cathode and therefore have a speed distribution dependent on temperature.
• The speed of the electrons is not always the same which causes different pathways through the lens and so aberration.
• The sample thickness reduces the speed of the electrons increasing the wavelength and decreasing the detail.

Question 4

TEMs operate using wavelengths of about 0.1 nm.

Explain why operation at such wavelengths makes the instrument such an important research tool. (2)

Answer 4

The resolution is improved for shorter wavelengths or shorter wavelengths enable more detailed images.

0.1 nm is the same order of magnitude as the diameter of an atom.

Question 5

State and explain two factors that limit the detail in the image produce by a TEM.

(4)

Answer 5

Image not accurately focused / blurred

Due to electrons not all having the same speeds so focused to different points by the magnetic lenses.

Electrons slowed down passing through the sample.

Wavelength changes by different amounts as they pass through the sample so each wavelength diffracted differently.

Question 6

In the figure below, a beam of monoenergetic electrons is produced by thermionic emission from a wire filament in an evacuated tube. The beam is directed at a thin metal sample at normal incidence and it emerges from the sample in certain directions only, including its initial direction.

Name the physical process occurring at the thin metal sample in the figure above which shows the electrons behaving as waves. (1)

Answer 6

diffraction

Question 7

In the figure below, a beam of monoenergetic electrons is produced by thermionic emission from a wire filament in an evacuated tube. The beam is directed at a thin metal sample at normal incidence and it emerges from the sample in certain directions only, including its initial direction.

Explain why the electrons need to be monoenergetic in order for them to emerge in certain directions only.

(2)

Answer 7

the electrons in the beam must have the same wavelength

otherwise electrons of different wavelengths (or speeds/velocities/energies/momenta) would diffract by different amounts (for the same order)

Question 8

A transmission electron microscope (TEM) operating at an anode potential of 25kV is used to observe an image of a thin sample.

Describe and explain how the resolution of the image would change if the anode potential were increased.

(3)

Answer 8

any two of the first three mark points

increase of pd increases the speed (or velocity/energy/
momentum) of the electrons

(so) the electron wavelength would be smaller
(and) the electrons would diffract less (when they pass through the lenses)

and

the image would show greater resolution (or be more detailed)

Question 9

Figure 1 shows a diagram of the Michelson-Morley interferometer that was used to try to detect the absolute motion of the Earth through the ether (æther).

Light from the monochromatic source passes through the semi-silvered glass block and takes two different paths to the viewing telescope. The two paths, PM1 and PM2, are the same length. Interference fringes are observed through the viewing telescope.

Explain how the experiment provided a means of testing the idea that the Earth had an absolute motion relative to the ether.

Your answer should include:

• an explanation of why a shift of the fringe pattern was predicted
• a comparison of the results of the experiment to the prediction
• the conclusion about the Earth’s absolute motion through the ether. (6)

Answer 9

6 marks: A thorough and well communicated discussion using most of the statements in bullets 1,2, and 3

Bullet point 1 in question (Explanation of how shift expected)

1. PM2 lies in the direction of the Earth’s velocity
2. Speed of light different in the two directions
3. The time taken for light to travel from P to M2 and back to P would be greater than the time taken from P to M1 and back to P
4. If the speed of light depends on the Earth’s velocity through the ether
5. Rotating the apparatus through 90° would cause the time difference to reverse/change
6. When rotated there would be a change in the phase difference between the waves (at each point in the fringe pattern)

Bullet point 2 in the question (Results compared with prediction)

7. The apparatus was capable of detecting shifts of 0.05 fringe
8. No shift was detected then or in later experiments when apparatus rotated

Bullet point 3 in the question (Conclusions)

9. The experiment showed that there is no absolute motion
10. Ether did not exist so light travels without the need for a material medium
11. The Earth was dragging the ether with it

Many responses fail to demonstrate an understanding that the shift pattern is there in the first place and the shift occurs due to rotation of the apparatus

They often imply that the shift is due to differences in the distance travelled

Question 10

Describe how Newton used the corpuscular theory to explain the refraction of light as it passes from one substance into a substance of higher optical density.

(3)

Answer 10

Appreciation that one component changes speed while the other component at right angles does not

When entering a denser medium a corpuscle / light accelerates or its velocity / momentum increases perpendicular to the interface

There is a (short range) attractive force between light corpuscle and the (denser) material

• Not allowed:*
• Attraction due to opposite charges*
• Force making them move faster is not enough*
• Accelerate in medium*
• Not gains energy*

Question 11

Huygens used a wave theory to explain refraction.

Explain why the corpuscular theory was rejected in favour of a wave theory to explain refraction. (2)

Answer 11

Light (was shown by experiment to) travel slower in (optically) denser medium OWTTE

Condone ‘waves..’ instead of ‘light’

OWTTE e.g. speed in vacuum higher than speed in other medium

Newton’s theory required light to travel faster, wave theory suggested slower speed
or
Newton’s theory could not explain the slower speed
or
Huygens theory could explain the slower speed

• Not allowed:*
• Reference to Young’s two slit- question asks them about refraction*

Question 12

Describe and explain the difference in the appearance of the fringes in Young’s double-slit experiment that are predicted by the corpuscular theory and by the wave theory for light.

(2)

Answer 12

A corpuscular theory predicts only two (bright) lines / high intensity patches of light whereas a wave theory predicts many fringes

Corpuscles can only travel in straight lines
or
waves can produce fringes because (diffract and) interfere / superpose / arrive in and out of phase / have different path differences

Need to describe the patterns ie not just interference fringes are seen for the first mark

Question 13

The magnetic flux density is adjusted until the beam passes through the two fields without deflection. Show that the speed v of the electrons when this occurs is given by

v = E/B

where E is the electric field strength and B is the magnetic flux density. (3)

Answer 13

magnetic force = Bev (1)

electric force = eE (1)

Bev = eE (gives v = E/B) (1)

Badly written but balance electric and magnetic force

Question 14

Cathode ray experiment : Describe how the charged particles responsible for conduction in the gas are produced.

(2)

Answer 14

electrons pulled out of (gas) atoms so (gas) atoms become (+) ions
OR
ionisation by collision (also) occurs
OR
(+) ions (that) hit cathode causing it to release electrons

conduction due to electrons and positive ions

; Allow ‘electrons ionise atoms’ as compensation mark
(if no marks elsewhere)

Question 15

Cathode ray experiment: Explain why the gas emits light and why it must be at low pressure. (3)

Answer 15

ions and electrons (moving in opposite directions) collide (with each other) and recombine and emit photons ✓

Owtte

electrons excite gas atoms (by collision )
and photons are emitted when de-excitation occurs ✓

If light not photons given in 1st 2 mark points, 1 max for 1st two mark points

gas needs to be at sufficiently low pressure in order that the particles (or uncharged gas atoms / ions / electrons) in the gas are widely spaced ✓

Owtte

otherwise (+) ions and / or electrons / particles would be stopped by gas atoms OR so that ions / electrons are accelerated (or gain enough ke) to cause excitation ✓

Question 16

Cathode ray experiment: The charged particles moving towards the negative electrode were initially referred to as positive rays. Explain why their specific charge depends on the choice of gas in the tube. (2)

Answer 16

Specific charge = charge / mass (and charge(s) of ion does not depend on the type of gas) ✓

Mass of ion depends on the type of gas ✓

Accept Q / m in symbols Q / m but not e / m if e / m is specifically stated as specific charge

Question 17

At the time when Thomson measured the specific charge of the particles in cathode rays, the largest specific charge known was that of the hydrogen ion.

State how Thomson’s result for the specific charge of each particle within a cathode ray compared with that for the hydrogen ion and explain what he concluded about the nature of the particles. (2)

Answer 17

The specific charge of the cathode rays/the particles was( much) larger/greater than the hydrogen ion/proton ✔

This provided evidence that cathode rays were composed of electrons/particles which have a (very) small mass / have a high (negative) charge

OR

Mass (much) smaller than the mass of a hydrogen (ion)/proton ✔

Not higher

If mark 1 not given then 0 for the question

Not lightest as substitute for mass

Question 18

A student carries out Millikan’s oil drop experiment and obtains the following results for the charges on the oil drops that were investigated.

–9.6 × 10^–19 C

–12.8 × 10^–19 C

–6.4 × 10^–19 C

Discuss the extent to which the student’s results support Millikan’s conclusion and how the student’s conclusion should be different.

(3)

Answer 18

Millikan’s conclusion: Electron charge is (-)1.6 × 10-19 C (WTTE) ✓

The charge on each droplet is a whole number × 1.6 × 10-19 C which agrees with Millikan ✓

Student’s results suggest -3.2 x 10-19 C as smallest quantum of charge ✓

allow multiple or n, where n is an integer

Question 19

If the charge on an electron is known then its mass can be determined from the specific charge. Describe how Millikan’s experiment with charged oil droplets enables the electronic charge to be determined.

Include in your answer:

• the procedures used to determine the radius of a droplet and the charge on a droplet
• how the measurements made are used
• how the electronic charge can be deduced.

The quality of your written communication will be assessed in your answer. (6)

Answer 19

A
Measure the terminal speed of the falling droplet
At the terminal speed weight = viscous force (+ upthrust)

mg = 6πƞrv and m = 4πr3ρ / 3 so r^2 = 9ƞv /2ρg

r could be determined as density of drop, viscosity of air and g are known (r is the only unknown)

B
m can be determined if r is known

Apply pd between the plates so electric field = V / d and adjust until droplet is stationary

QV / d = mg so Q can be found

C
Make a number of measurements to find Q

Results for Q are in multiples of 1.6 × 10−19C so Q can be found

Question 20

The diagram shows a gas discharge tube devised by William Crookes in one of his investigations.

When a large potential difference is applied between the cathode and anode the paddle wheel is seen to rotate and travel along the rail towards the anode.

Explain how this experiment led Crookes to conclude that cathode rays are particles and that these particles caused the movement of the paddle. (2)

Answer 20

Cathode rays/electrons move from cathode toward anode

Accept move left to right.

The paddle wheel has gained energy from cathode rays/electrons. ✔

Accept as alternatives for energy kinetic,

energy/momentum/impulse ✔

• Ignore references to force.*
• Ignore references to applying a magnetic field.*

Question 21

Later experiments showed that cathode rays are electrons in motion.

Explain how cathode rays are produced in a gas discharge tube.

(3)

Answer 21

Electrons are pulled out/escape from atoms OR gas atoms are ionised ✔

Condone molecules as alternative to atoms.

(Positive ions generated near the cathode are attracted to the cathode causing free) electrons emitted from the cathode.✔

Electrons are accelerated toward the anode (by the potential difference) ✔

Do not accept attraction as an alternative to acceleration.

Question 22

In a particular gas discharge tube, air molecules inside the tube are absorbed by the walls of the tube.

Suggest the effect that this absorption may have on the motion of the paddle wheel.

Give a reason for your answer. (2)

Answer 22

Reason: Idea of fewer electrons/cathode rays ✔

Effect: Paddle wheel rotates less ✔

Must score the reason mark to score the effect mark.

Ignore references to air resistance.

OR

Reason: Idea of electrons/cathode rays have higher energy/speed/momentum ✔

Effect: Paddle wheel rotates more ✔

If no mark is awarded, one mark can be awarded for the effect of the paddle wheel rotating more where the reasoning is limited to less collisions of electrons with air molecules.

Question 23

If an electron of this energy (accelerated by 2200v) was to impinge on a fluorescent screen, calculate the shortest wavelength of the electromagnetic radiation subsequently emitted and explain why this is a minimum value.

(3)

Answer 23

all the k.e. goes to one photon (1)
hf = k.e. [or 3.5 × 10^–16 J] (1)

λ = c/f (1)

Question 24

Millikan:

The mass of another charged droplet was found to be 4.3 × 10–15 kg. With switch S closed and the voltage supply at its maximum value of 1000 V, this droplet fell more slowly than when the switch was open but it could not be stopped.

Explain why this droplet could not be held at rest and show that the magnitude of the charge on it was 1.6 × 10–19 C. (4)

Answer 24

The weight of the second droplet is greater than the maximum electric force on it

Alternative for 1st mark;

weight = drag force + elec force ( owtte)

Scheme using V for next 5 marks;

If n =1 for the second droplet , pd to hold it = 1580 V ( = mgd / e)

which is not possible as V max = 1000 V

If n = 2 , it would be held at rest by a pd of 790 V ( = 1580 / 2 or 680 × 4.3 / 3.7 V)

if n > 2 , it would be held at rest by a pd of less than 790 V ( or 790 / n V)

So n =1(e ) must be the droplet charge

Question 25

In a scanning tunnelling microscope (STM), a metal probe with a sharp tip is scanned across a surface, as shown in the figure below.

Explain why electrons transfer between the tip of the probe and the surface when the gap between the tip and the surface is very narrow and a pd is applied across it.

(3)

Answer 25

electrons have a wave-like nature (1)
there is a (small) probability that an electron can cross the gap
[or an electron can tunnel across the gap] (1)
transfer is from - to + only (1)

Question 26

In a scanning tunnelling microscope (STM), a metal probe with a sharp tip is scanned across a surface, as shown in the figure below.

Describe how an STM is used to obtain an image of a surface.

(3)

Answer 26

constant height mode:

gap width varies as tip scans across at constant height (1)
current due to electron transfer is measured (1)
current decreases as gap width increases (or vice versa) (1)
variation of current with time is used to map surface (1)

or constant current mode:

current due to electron transfer is measured (1)
feedback used to keep current constant
by changing height of probe tip (1)
height of probe tip changed to keep gap width constant (1)
variation of height of probe tip with time
used to map surface (1)

Question 27

Discuss the historical relevance of the value of the specific charge of the electron compared with the specific charge of the H+ ion. (2)

Answer 27

specific charge for the electron ≈ 2000 × specific charge of H+

(accept = and accept any value between 1800 and 2000) which was the largest known specific charge before the specific charge of the electron was determined/measured

concluded from the experiment that electrons have relatively low mass or high charge

Question 28

Explain why electrons can cross the gap between the tip of the probe and the surface in a TEM

provided

• the gap is sufficiently narrow
• a potential difference is applied between the tip and the surface.

The quality of your written communication will be assessed in this question. (6)

Answer 28

• electrons have a wave like nature
• there is a finite probability that electrons can cross the gap
• electrons can tunnel across the gap
• pd is necessary so electrons cross in one direction only (no net transfer of electrons for zero pd)
• the narrower the gap, the greater the number of electrons (per second) that cross the gap
• electrons transfer from - to +
• constant pd provides one less variable (to affect the current) (de Broglie) wavelength is of the order of the gap width

Question 29

Newton’s corpuscular theory predicted incorrectly that just two bright fringes would be formed in this pattern - double slit experiment (with coherent source). Use Huygens’ theory of light to explain why more than two bright fringes are formed in this pattern.

The quality of your written communication will be assessed in this question. (6)

Answer 29

the pattern is due to interference of light from the two slits

interference is a wave property

light from the two slits is in phase at a bright fringe and therefore reinforces

the path difference (from the central bright fringe to the two slits) is zero

either bright fringes are formed away from the centre wherever the path difference is a whole number of wavelengths or dark fringes are formed away from the centre wherever the path difference is a whole number of wavelengths + a half wavelength

the path difference for the mth bright fringe from the centre is m wavelengths where m is any whole number

since m is any whole number, more than two bright fringes are observed

Question 30

State De Broglie’s hypothesis (2)

Answer 30

(Matter) particles have wave-like properties (owtte) 

and an associated wavelength = h / p where p is the momentum of the particles .

Question 31

State the appropriate voltages used for heating a filament for thermionic emission, and then that for accelerating these electrons (2)

Answer 31

• thermionic emission : 0 -50V
• accelerating : >250V

Question 32

The diagram shows a gas discharge tube devised by William Crookes in one of his investigations.

When a large potential difference is applied between the cathode and anode the paddle wheel is seen to rotate and travel along the rail towards the anode.

Explain how this experiment led Crookes to conclude that cathode rays are particles and that these particles caused the movement of the paddle. (2)

Answer 32

Cathode rays/electrons move from cathode toward anode

Accept move left to right.

The paddle wheel has gained energy from cathode rays/electrons.

Question 33

J J Thomson devised the first experiments to determine the specific charge for cathode rays produced in discharge tubes. He found that the value did not depend on the gas in the tube. He also discovered that particles emitted by a heated filament and particles emitted in the photoelectric effect had the same specific charge.

State two conclusions that were drawn from Thomson’s experiments. (2)

Answer 33

Experiments suggested cathode rays were negatively charged particles ✔

Particle has mass much smaller than mass of an atom / hydrogen ion

OR

Compares Specific charge with that of hydrogen ion / atom ✔

Particles were part of the substructure of matter / atoms ✔

Particles emitted in each case were the same

OR

Particles emitted were the same for different gases / for photoelectrons and particles from thermionic emission ✔

Question 34

The solid line on the graph below shows how the intensity of radiation from a black body varies with wavelength at a particular temperature. The dotted line shows the variation as predicted by classical physics.

Explain why the difference between the predicted and experimental curves is called the ultraviolet catastrophe. (2)

Answer 34

The observed and prediction using classical physics do not agree for short wavelengths.✔

This disagreement is in the ultraviolet part of the spectrum.✔

Question 35

Describe the difference between the classical physics view and the quantum theory proposal made by Max Planck that enabled the distribution of the shape of the intensity−wavelength graph to be correctly predicted. (2)

Answer 35

In classical physics radiation is emitted as a continuous wave.✔

Planck proposed that energy is emitted in discrete packets/quanta.

or

Proposed that the energy of a quantum is hf where f is the frequency of the radiation.✔

Question 36

Why does Maxwells formula show that light is an EM wave? (2)

Answer 36

E₀ relates to the electric field strength due to a charged object in free space

µ₀ relates to the magnetic flux density due to a current-carrying wire in free space.

Question 37

Describe how Newton used the corpuscular theory to explain the refraction of light as it passes from one substance into a substance of higher optical density. (2)

Answer 37

Appreciation that one component changes speed while the other component at right angles does not ✓

When entering a denser medium a corpuscle / light accelerates or its velocity / momentum increases perpendicular to the interface ✓

There is a (short range) attractive force between light corpuscle and the (denser) material ✓

Question 38

With the aid of a diagram, explain what is meant by an electromagnetic wave. (3)

Answer 38

diagram to show sinusoidal E and B fields at 90° to each other (1)
direction of propagation perpendicular to E and B (1)
E and B waves in phase (1)

Question 39

Electrons are emitted by the cathode by thermionic emission. They are accelerated by the potential difference between the cathode and anode. The tube contains helium gas at a low pressure and the gas emits light to show the path of the electron beam.

The beam is bent into a circular path by applying a magnetic field perpendicular to the plane of the diagram.

In practice the path of the electron beam is not a perfect circle.

Discuss how the presence of the gas affects the path of the electrons. (3)

Answer 39

Electron velocity decreases when they collide.✔

v is proportional to r

OR r = vm/Be and m, B and e are constant.✔

r (gradually) decreases

or path with be an inwards spiral.✔