Please cite as: Fletcher, P.R., (1997) Master of Science Thesis - How Students Learn Quantum Mechanics (School of Physics, University of Sydney)

A1-81

APPENDIX 1

PHYSICS 1/1A - ATOMIC AND NUCLEAR PHYSICS QUIZ

This Appendix contains a copy of a preliminary instrument which was

administered to 242 first year physics students at the University of Sydney in 1994.

There were a number of different types of quizzes given to students at various

stages of their courses in 1993 and 1994 relating to quantum mechanics. This quiz

was chosen as the starting point of the current study because it was a

straightforward multiple choice quiz taken by students studying the material for the

first time.

Presented in this Appendix are:

• the Physics 1/1A Atomic and Nuclear Physics Quiz questions, • the Answer Sheet, • the “Official” Answers and, • a summary of results to the multiple choice responses.

A1-82

PHYSICS 1/1A

Atomic and Nuclear Physics — Quiz INSTRUCTIONS • Don't guess. Make a note of your reasons for each answer. • Mark all your answers on this question paper before writing on the answer sheet. • Only when you are satisfied with your answers, copy them onto the answer sheet. • Hand in the completed answer sheet only. • Check your answers against the check list which will be provided. This test will not in any way contribute to your final assessment. In the following questions, only one statement is correct and relevant. Identify that statement in each case by writing T (true) in the appropriate box. (1) In the photoelectric effect, even if the incident beam is highly monochromatic

(ie. all parts of the beam oscillate with the same frequency), the ejected photoelectrons come off with many different energies. This is because

❏ A. all the atoms in the solid are not initially in their ground state.

❏ B. most electrons that can escape will lose energy by collisions before they get

out.

❏ C. the work function of the material varies throughout the solid.

(2) In the photoelectric effect a cut-off frequency is always observed. Why do we

believe that this speaks in favour of the particle theory of light rather than the wave theory?

❏ A. Because electromagnetic radiation of very low frequency cannot give

energy to electrons.

❏ B. Because only particles with more than a minimum energy can give the

electrons enough energy to escape.

❏ C. Because a low frequency electromagnetic wave must be able to give any

amount of energy to an electron, if its amplitude is large enough. (3) Nowadays we say that light behaves like a particle, as well as like a wave.

What is meant by that statement?

❏ A. Light sometimes shows some of the properties that we normally associate

with billiard balls or point masses.

❏ B. Light sometimes can be measured to have velocity, energy and

momentum.

A1-83

❏ C. Light sometimes does NOT show effects like interference and diffraction.

A1-84

(4) Assume that the emission of photons from a source of radiation is random in direction. Would you expect the intensity of this light to vary inversely as the square of the distance, as in the wave theory?

❏ A. No, because in the particle theory, since there are only a limited number of

photons, they cannot spread out into all directions.

❏ B. Yes, because photons are really waves, and therefore they will show this

wave-like property.

❏ C. Yes, because they will spread out over the surface of a sphere whose area

is proportional to radius squared. (5) In the Bohr model of a hydrogen atom, the lowest energy state has the

smallest radius. However an electron has a higher velocity in an orbit which is closer to the nucleus, and therefore its kinetic energy is larger in this orbit. These statements are not in conflict because

❏ A. the electrostatic force on the electron is attractive, therefore the kinetic

energy is negative, and the lowest energy is that which is largest and negative.

❏ B. the potential energy is higher when the electron is further from the

nucleus, and this more than compensates for the lower kinetic energy.

❏ C. in any real atom, the electron in an orbit behaves like a wave, and

therefore the calculation of kinetic energy is not appropriate. (6) Nowadays we say that electrons and protons behave like waves, as well as

like particles. What is meant by that statement?

❏ A. Electrons and protons sometimes do not show some of the properties that

we normally associate with billiard balls or point masses.

❏ B. Electrons and protons sometimes cannot be measured to have velocity,

energy and momentum.

❏ C. Electrons and protons sometimes show effects like interference and

diffraction. (7) Quantum effects are not normally observed in real life because the magnitude

of the Planck constant is so small. However if it were much, much larger (say, of order 1 Joule.sec) you might notice such effects with billiard balls. Which of the following do you think you might observe?

❏ A. The position of the balls would be uncertain and you wouldn't be able to

hit them easily with a billiard cue.

❏ B. The balls would spread out and go into more than one side pocket.

❏ C. The balls could only exist with discrete kinetic energy levels and therefore

you wouldn't be able to hit them gently.

A1-85

ANSWER SHEET

Atomic and Nuclear Physics — Quiz INSTRUCTIONS • Mark your answer on the question paper first. • Only when you are satisfied with your answers copy them onto this sheet. • Mark each answer by entering a clear tick in the appropriate box. • Please do not make alterations on this sheet. If you make a mistake ask for a new answer

sheet. • When you hand in this sheet you will be given a copy of the official answers.

NAME (optional): __________________________ SID: _____________________

Physics 1 or 1A class — tick one:

1(A) pm Tue, Wed, Thu Theatre 8 (ground floor) Davis ❏

1(N) pm Tue, Wed, Thu Theatre 1 (2nd floor) Pongracic ❏

1(N) am Mon, Wed, Fri Theatre 8 (ground floor) Cross ❏

1(N/E) am Tue, Thu, Fri Theatre 1 (2nd floor) Booth ❏

ANSWERS

(1) A. ❏ B. ❏ C. ❏

(2) A. ❏ B. ❏ C. ❏

(3) A. ❏ B. ❏ C. ❏

(4) A. ❏ B. ❏ C. ❏

(5) A. ❏ B. ❏ C. ❏

(6) A. ❏ B. ❏ C. ❏

(7) A. ❏ B. ❏ C. ❏

A1-86

A1-87

OFFICIAL ANSWERS Atomic and Nuclear Physics — Quiz

SCORING: 1 mark for each correct answer; –1 mark for each incorrect answer; 0 for each blank answer. Question Correct

answer Reason

1 B The free electrons which take part in electrical conduction initially have very small thermal kinetic energies. So when they absorb a photon their total energy is hf. Most will collide with other electrons before escaping. Their energy can only decrease by such a collision, never increase since those they collide with have such small energy.

2 C There is no (simple) reason why a low frequency wave of sufficiently large amplitude should not be able to give any desired amount of energy to an electron. If experiment shows that low frequency light cannot give electrons enough energy to escape, no matter how intense the beam, it is not behaving like a wave.

3 A All three items are true, but only A answers the question. Waves can have velocity, energy and momentum; and there are plenty of instances where, for example, water waves do not show interference or diffraction.

4 C The intensity of light is the rate of energy crossing unit area. For energy travelling in all directions, the energy spreads out over the area of a sphere which depends on r2. Hence the intensity is inversely proportional to r2.

5 B Kinetic energy must always be positive. In this system, the electrostatic force is attractive, and the potential energy is (by convention) twice as large (in magnitude) as the kinetic energy, and negative. Hence the result. Item C is true but irrelevant. The electron in its orbit shows both wave and particle properties. The relation between energy and distance is the particle-like property it shows.

6 C All three items are true, but only C answers the question. An entity which does not behave like a point mass, and for which you cannot measure velocity, energy and momentum does not have to be a wave. There are many other things it could be. But interference or diffraction are absolutely characteristic of the way waves behave.

7 A Any answer here is debatable. Probably the uncertainty in position of a billiard ball would be such to make A true. Item B could not be true without the ball's breaking up (it would still behave like a particle as well as a wave). Item C need not necessarily be true unless there were an attractive force acting on the ball, as if it were inside an "atom".

A1-88

A1-89

Physics 1/1A :: Atomic and Nuclear Physics Quiz

Result Summary of Multiple Choice Responses by Class

Class A B C NR Sample Question 1 C1 40 55 5 0 55

C2 18 78 4 0 72 C3 49 42 7 2 57 C4 17 69 12 2 58 Total 30 62 7 1 242 A B C NR

Question 2 C1 11 55 33 2 55 C2 6 64 31 0 72 C3 5 81 11 4 57 C4 10 43 43 3 58 Total 8 61 29 2 242 A B C NR

Question 3 C1 58 38 2 2 55 C2 42 47 11 0 72 C3 42 42 14 2 57 C4 55 31 9 5 58 Total 49 40 9 2 242 A B C NR

Question 4 C1 7 11 78 4 55 C2 10 22 67 1 72 C3 14 28 54 4 57 C4 14 24 57 5 58 Total 11 21 64 3 242 A B C NR

Question 55 C1 18 60 22 0 55 C2 22 57 21 0 72 C3 19 46 33 2 57 C4 19 69 7 5 58 Total 20 58 21 2 242 A B C NR

Question 6 C1 7 20 71 2 55 C2 19 10 71 0 72 C3 21 5 72 2 57 C4 29 3 67 0 58 Total 19 10 70 1 242 A B C NR

Question 7 C1 62 7 31 0 55 Shaded area denotes the correct response C2 50 3 46 1 72 Bolded denotes the highest % response C3 25 5 67 4 57 C1 - Physics 1A Advanced Stream C4 57 5 29 9 58 C2 thru C4 - Physics 1 Normal Stream Total 48 5 43 3 242 A, B, C - Response NR - No Response Sample - 242

Table A1-1 : Tabulated results for the preliminary instrument administered to first year physics students in 1994.

A1-90

Physics 1/1A :: Atomic and Nuclear Physics Quiz Result Summary of Multiple Choice Responses

Summary of Question

Correct Answer and the Major Distracter (if present) A B C N

Q1 Photoelectric effect Why are photoelectrons ejected with different energies? Correct Response - (b) most electrons that can escape will lose energy by collisions before they get out Major Distracter - (a) all the atoms in the solid are not initially in their ground state

30

62

7

1

Q2 Photoelectric effect Why does cut off freq favour the particle theory? Correct Response - (c) because a low frequency electromagnetic wave must be able to give any amount of energy to an electron, if its amplitude is large enough Major Distracter - (b) because only particles with more than a minimum energy can give the electrons enough energy to escape

8

61

29

2

Q3 Light behaves like a particle and a wave. What is meant by this statement? Correct Response - (a) light sometimes shows some sort of the properties that we normally associate with billiard balls or point masses. Major Distracter - (b) light sometimes can be measured to have velocity, energy and momentum

49

40

9

2

Q4 Photon emission Would you expect the intensity of light to vary inversely as the square of the distance? Correct Response - (c) Yes, because they spread out over the surface of a sphere whose area is proportional to radius squared

11

21

64

3

Q5 Bohr model Concerning the energy of an electron in different orbits (refer to Appendix 1 page A1-3 for question details)

20

58

21

2

Q6 Electrons and protons behave like waves and particles What is meant by the statement? Correct Response - (c) electrons and protons sometimes show effects like interference and diffraction

19

10

70

1

Q7 Planck’s constant What would you observe if it was larger? Correct Response - (a) the position of the balls would be uncertain and you wouldn’t be able to hit them easily with a billiard cue Major Distracter - (c) the balls could only exist with discrete kinetic energy levels and therefore you wouldn’t be able to hit them gently

48

5

43

3

Shaded area denotes the correct response Bolded denotes the highest % response Sample - 242

Table A1-2 : Tabulated summary of results for the preliminary instrument administered to first year physics students in 1994.

APPENDIX 1...................................................................................................................................... 81

A1-91

PHYSICS 1/1A - ATOMIC AND NUCLEAR PHYSICS QUIZ....................................................... 81 TABLE A1-1 : TABULATED RESULTS FOR THE PRELIMINARY INSTRUMENT ADMINISTERED TO FIRST YEAR

PHYSICS STUDENTS IN 1994. ......................................................................................................... 89 TABLE A1-2 : TABULATED SUMMARY OF RESULTS FOR THE PRELIMINARY INSTRUMENT ADMINISTERED

TO FIRST YEAR PHYSICS STUDENTS IN 1994. ................................................................................. 90