Quantum Physics Practice Problems PSI AP Physics B Name______________________________

1. A “Cathode Rays” experiment is associated with:

(A) R. A. Millikan

(B) J. J. Thomson

(C) J. S. Townsend

(D) M. Plank

(E) A. H. Compton

2. The electron charge was measured the first time in:

(A) Cathode ray experiment

(B) Photoelectric effect experiment

(C) Oil drop experiment

(D) Diffraction electrons from aluminum foil

(E) Compton effect experiment

3. Which of the following colors associated with the lowest temperature?

(A) Violet

(B) Blue

(C) Green

(D) Yellow

(E) Red

4. Which of the following photons has the greatest energy?

(A) Infrared

(B) Blue

(C) X-Ray

(D) γ- photon

(E) UV – photon

5. The energy of a photon depends on:

(A) Amplitude

(B) Speed

(C) Temperature

(D) Pressure

(E) Frequency

6. How does the energy of a photon change if the wavelength is doubled?

(A) Doubles

(B) Quadruples

(C) Stays the same

(D) Is cut to one-half

(E) Is cut to one-fourth

7. How does the momentum of a photon change if the wavelength is halved?

(A) Doubles

(B) Quadruples

(C) Stays the same

(D) Is cut to one-half

(E) Is cut to one-fourth

8. The photoelectric effect explains :

(A) The wave nature of light

(B)The particle nature of light

(C) The wave properties of an electron

(D) The particle properties of an electron

(E) The atomic structure

9. The kinetic energy of photo-electrons depends on:

(A) Speed of light

(B) Angle of illumination

(C) Intensity of light

(D) Work function

(E) Wavelength

10. Which of the following is the formula of the photon mass?

(A) m = h/cλ

(B) m = cλ/h

(C) m = h/f

(D) m = f/h

(E) m = Ec2

11. The maximum kinetic energy of photo-electrons depends on which of the following:

I. The light intensity

II. The frequency of the light

III. The nature of the photo-cell

(A) Only I (B) Only II (C) Only III (D) Only I and II (E) Only II and III

12. Which of the following formulas explains the photo-electric effect?

(A) hλ = W0 + KE

(B) hf = W0 - KE

(C) hf = W0 + KE

(D) hλ = -W0 + KE

(E) hc/λ = W0 - KE

13. Which of the following graphs is a correct relationship between the maximum kinetic energy of

photo-electrons and the frequency of the incident light?

(A) (B)

(C) (D)

(E)

14. Which of the following graphs is a correct relationship between the maximum kinetic energy of

photo-electrons and the intensity of the incident light?

(A) (B)

(C) (D)

(E)

15. Which of the following graphs is a correct relationship between the de Broglie wavelength and

the linear momentum of a particle?

(A) (B)

(C) (D)

(E)

16. All of the following are properties of γ-rays EXCEPT:

(A) They discharge electrified objects

(B) They ionize gases

(C) They are deflected by magnetic fields

(D) They penetrate light objects

(E) They are diffracted by crystals

17. Which of the following phenomena provides the best evidence that light can have particle

properties?

(A) Diffraction of light

(B) Electromagnetic radiation

(C) Compton effect

(D) Electron diffraction

(E) γ-ray diffraction

18. Which of the following phenomena provides the best evidence that particles can have wave

properties?

(A) The absorption of photons by electrons in an atom

(B) The alpha-decay of radioactive nuclei

(C) The interference pattern produced by neutrons incident on a crystal

(D) The production of x-rays by electrons striking a metal target

(E) The scattering of photons by electrons at rest

19. Which of the following formulas can be used to determine the de Broglie wavelength?

(A) λ = hmv

(B) λ = h/mv

(C) λ = mv/h

(D) λ = hm/c

(E) λ = mc/h

20. A photon can disappear producing an electron and proton, this phenomenon is called?

(A) Interference of light

(B) Diffraction of X-Rays

(C) Pair production

(D) Scattering of electrons

(E) Annihilation

21. When a proton collides with an electron they disappear producing photons, this phenomenon is

called?

(A) Interference of light

(B) Diffraction of X-Rays

(C) Pair production

(D) Scattering of electrons

(E) Annihilation

22. The following statement: “In order to understand a given experiment, we must use either the

wave or the photon theory, but not both” is called?

(A) Wave theory of light

(B) Particle theory of light

(C) Planetary theory of an atom

(D) Principle of complementarity

(E) Wave theory of matter

23. Electrons are accelerated to a maximum speed of v in an X-Ray tube by an applied voltage V0.

What is the maximum speed of the electrons if the voltage is quadrupled?

(A) 4v

(B) 2v

(C) 𝑣

√2

(D) √2 v

(E) v/4

24. In a Compton Effect experiment a photon scattered from an electron at rest increases its

wavelength from λi to λf. Which of the following deflecting angles ϴ gives the greatest raise in

the wavelength of the scattered?

(A) 0 ̊ (B) 30 ̊ (C) 60 ̊ (D) 90 ̊ (E) 180 ̊

25. Which one of the following objects moving at the same speed is associated with a greatest

wavelength?

(A) Neutron (B) Electron (C) Tennis ball (D) Bowling ball (E) α- Particle

26. According to the Bohr model of the atom, the angular momentum of an electron is:

(A) Linearly increases with increasing electron’s velocity

(B) Linearly increases with increasing orbital radius

(C) Quantized

(D) Inversely proportional to the electron’s velocity

(E) Inversely proportional to the orbital radius

27. A Rutherford’s experiment “Scattering α–particles by a gold foil” was conducted to prove which

of the following:

(A) Plum-pudding model of the atom

(B) Planetary model of the atom

(C) De Broglie hypothesis

(D) Wave nature of light

(E) Quantum theory of light

28. In the Rutherford’s Experiment “Scattering α – particles by a gold foil” the biggest part of α –

particles could pass through the foil undeflected. Which of the following properties of the atom

can be explained from this observation?

(A) The positive charge is concentrated in the nucleus

(B) The nucleus has electrons and protons

(C) The atomic mass is concentrated in the nucleus

(D) The α – particles couldn’t be deflected by electrons

(E) The size of the nucleus is much less than the size of the atom

29. Which of the following statement(s) can be associated with Bohr’s theory of the atom?

I. An electron orbiting the nucleus can change its energy continuously

II. An electron orbiting the nucleus emits energy and falls on the nucleus

III. An electron orbits the nucleus without radiating energy and can change its

energy only by a certain portion when it jumps between the orbits

IV. The angular momentum of an electron around the nucleus is equal an integer

times h/2π

(A) I and II (B) II and IV (C) II and III (D) III and IV (E) I, II, III and IV

30. When an electron falls from an orbit where n = 2 to n = 1:

(A) A photon is emitted

(B) A photon is absorbed

(C) No change in atomic energy

(D) Atomic energy decreases to zero

(E) Atomic energy increases

31. When an electron jumps from an orbit where n = 1 to n = 3 its orbital radius in terms of the

smallest radius r1 is:

(A) r1/9 (B) r1/3 (C) 2 r1 (D) 3 r1 (E) 9 r1

32. When an electron jumps from an orbit where n = 1 to n = 4 its energy in terms of the energy on

the ground level is:

(A) E1/9 (B) E1/16 (C) 2 E1 (D) 4 E1 (E) 16 E1

33. An electron is moving around a single proton in an orbit characterized by n = 5. How many of the electron's de Broglie wavelengths fit into the circumference of this orbit? (A) 3 (B) 4 (C) 5 (D) 16 (E) 25

34. In a cathode ray tube an electron is accelerated by an electric field. When the applied voltage is

600 V the electron’s De Broglie wavelength is λ. What is the De Broglie wavelength of the

accelerated electron through a potential difference of 150 V?

(A) λ (B) 2 λ (C) λ /2 (D) λ /4 (E) 4 λ

35. According to the Maxwell’s theory of electro-magnetism an electron orbiting the atomic nucleus

is:

(A) Changes its energy by certain portions

(B) Conserves its angular momentum

(C) Conserves its energy

(D) Radiates its energy and falls on the nucleus

(E) Changes its angular momentum by certain portions

36. A hypothetical atom has the energy levels presented by the graph. An electron is excited from

the ground state to the energy level -1 eV. The following are the energies of the emitted

photons EXCEPT:

(A) 9 eV (B) 4 eV (C) 6 eV (D) 2 eV (E) 10 eV

37. A hypothetical atom has energy levels presents by the graph. A container with the hypothetical

gas is irradiated with electro-magnetic radiation with the energy range from 4 eV to 9 eV. The

following sequence of the photons can be found in the emission spectrum.

(A) 1 eV, 2 eV, and 6 eV only

(B) 2 eV, 3 eV, and 4 eV only

(C) 1 eV, 3 eV, and 5 eV only

(D) 7 eV and 2 eV only

(E) None from the above

38. A hypothetical atom has energy levels presents by the graph. A container with the hypothetical

gas is irradiated with electro-magnetic radiation with the energy range from 4 eV to 9 eV. Which

of the following transitions will produce a photon with the longest wavelength?

(A) From n = 4 to n = 1

(B) From n = 4 to n = 2

(C) From n = 2 to n = 1

(D) From n = 3 to n = 1

(E) From n = 4 to n = 3

39. According to the Bohr’s theory of the hydrogen atom, electrons starting in the 4th energy level

and eventually ending in the ground state could produce a total of how many lines in the

hydrogen spectra?

(A) 6 (B) 5 (C) 7 (D) 4 (E) 3

40. Which of the following transitions is related to the energy absorption?

(A) α1 (B) α2 (C) α3 (D) α4 (E) α5

General Problems

1. In an experiment conducted to investigate a photo-electric effect physic students use an

apparatus show on the diagram. Photo-electrons emitted as a result of incident light can be

accelerated or stopped by an applied voltage. When the incident light has a wavelength of 300

nm the stopping voltage required to stop them is 1 V. If the incident light has a wavelength of

200 nm the stopping voltage is 3 V.

a. Calculate the Plank’s constant from the data collected in the experiment.

b. Calculate the work function for the photo-cell use in the experiment.

c. Determine the threshold frequency for this type of photo-cell.

d. Calculate the stopping voltage required to stop photo-electrons emitted by the

cell when the incident light has a wavelength of 100 nm.

2. A group of physics students conducts an experiment to investigate a photo-electric effect. They

graphed the kinetic energy as a function of frequency of the incident light.

a. Determine the Plank’s constant from the given graph.

b. Determine the work function of the photo-cell.

c. Determine the threshold frequency.

In the second trial students use a photo-cell with greater work function

d. How does it change the graph? Explain.

3. An electromagnetic radiation is incident on a metallic surface and electrons are emitted by the

plate when the wavelength is 450 nm or less.

a. What is the work function of the metal?

b. What is the maximum kinetic energy of photo-electrons if the incident light has

a wavelength of 400 nm?

c. What is the stopping voltage required to stop photo-electrons ejected by the

plate when the incident light has a wavelength of 300 nm?

d. If the stopping voltage is 5 V, what is the wavelength of the incident light?

4. An X-Ray photon with a wavelength of λi = 0.14 nm collides with a electron at rest and bounces

back.

a. What is the wavelength of the scattered photon?

b. What is the momentum of the recoil electron?

c. What is the energy of the recoil electron?

d. Is the energy conserved during the collision?

e. What is the De Broglie wave length of the scattered electron?

5. An X-Ray tube accelerates an electron beam between two electrodes. A 70,000 V potential

difference is applied across the tube.

a. What is the speed of the accelerated electrons?

b. What is the energy of the emitted photons?

c. What is the wavelength of the emitted photons?

d. What is the mass of the emitted photons?

e. What is the momentum of the emitted photons?

6. A free electron is captured by a proton. As a result of this process two photons are emitted. The

energy of the first photon is E1 = 3.4 eV.

a. Calculate the wavelength of the photon with energy E1.

b. Calculate the energy of the second photon E2.

c. Calculate the wavelength of the second photon?

d. On the diagram below show arrows associated with these transitions of the

electron.

The electron stays on the ground level for a long limit of time and then absorbs an energy of

15 ev from an incident photon.

e. What is the energy of the emitted electron?

f. What is the De Broglie wavelength of the emitted electron?

Multiple Choice Answers

1. B

2. C

3. E

4. D

5. E

6. D

7. A

8. B

9. E

10. A

11. E

12. C

13. C

14. A

15. E

16. C

17. C

18. C

19. B

20. C

21. E

22. D

23. B

24. E

25. B

26. C

27. A

28. E

29. D

30. A

31. A

32. B

33. C

34. E

35. D

36. D

37. C

38. E

39. A

40. D

Free Response

1. a. h = 4 x 10-15 eVs

b. WO = 3.14 eV

c. f = 7.6 x 1014Hz

V = 9.3 V

2. a. h = 4 x 10-15 eVs

b. WO = 3.1 eV

c. f = 0.75 x 1015 Hz

d. It shifts the graph to the right. The

slope is constant (h).

3. a. WO = 2.76 eV

b. 0.34 eV

c. 1.37 eV

d. λ = 160 nm

4. a. 1.45 x 10-10 m

b. 1.6 x 10-25 kg m/s

c. 1.4 x 10-20 J

d. λ = 413 nm

5. a. v = 1.57 x 108 m/s

b. E = 1.12 x 10-14 J or 7 x 104 eV

c. λ = 0.0177 nm

d. m = 1.2 x 10-31 kg

e. p = 3.7 x 10-23 kg m/s

6. a. λ = 365 nm

E = 10.2 eV

c. λ = 122 nm

d. An arrow from 0 eV to -3.4 eV and

another arrow from -3.4 eV to -13.6 eV

e. E = 1.4 eV or 2.24 x 10-19 J

f. λ = 1 nm