Physics



AP Physics 6: Subatomic Mass, Energy & Momentum Name __________________________

A. Atomic Nucleus

1. 2 types of particles—nucleons

a. positively charged proton and neutral neutron

b. rest mass chart (1 u = 1.66 x 10-27 kg)

|Object |kg |u |

|Proton (11p) |1.67262 x 10-27 |1.007276 |

|Neutron (10n) |1.67493 x 10-27 |1.008665 |

|Electron (0-1e) |9.1094 x 10-31 |0.00054858 |

2. nuclide (combination of protons and neutrons)

a. number of protons = atomic number (Z)

b. number of protons + neutrons = mass number (A)

c. nuclide symbol: AZX

1. X is atomic symbol with same Z number

2. A varies = isotopes

3. binding energy (BE) and nuclear forces

a. takes energy to break a stable nuclide into its parts ∴ energy is added to the nuclide to separate into protons and neutrons

1. nuclide + BE = protons + neutrons

2. change in mass, E = mc2

a. c = 3 x 108 m/s (speed of light)

b. if E = BE, then m = mBE in kg

c. mnuclide + mBE = mp + mn

b. binding energy per nucleon (BE/# nucleons)

[pic]

c. nuclear processes

1. exothermic when BE/#nucleon increases

2. mproducts – mreactants = mBE (-mBE is exothermic)

3. nuclear fission: Zsmall → Zlarge

a. thermonuclear devise—Hydrogen bomb

b. sun's energy

4. nuclear fission: Zlarge → Zsmall

a. atomic bomb (Hiroshima)

b. nuclear power plants

4. strong nuclear force

a. acts over a very short distance (10-18 m)

b. bind "up" and "down" quarks together

1. proton = 2 up (u+2/3) + 1 down (d-1/3) quark

2. neutron = 1 up (u+2/3) + 2 down (d-1/3) quark

proton neutron

c. binds neutrons and protons together

d. neutrons stabilize nuclide

1. electric repulsion between protons is significant when protons > 10-18 m apart

2. neutrons increase total strong nuclear force without increasing electric repulsion

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

5. naturally occurring radioactivity

a. unstable nuclides undergo nuclear change

b. nuclide is too large (Z > 84)

1. alpha radiation, 42α (42He)—low penetration

2. 22688Ra → 22286Rn + 42α

3. BE/# nucleons increases

c. A > average atomic mass

1. beta radiation, 0-1β- (0-1e)—medium penetration

a. d-⅓ → U⅔ + 0-1β-

b. 10n → 11p + 0-1β-

c. involves "weak nuclear force" and generates an additional particle called neutrino (ν)

2. 146C → 147N + 0-1β-

d. A < average atomic mass

1. positron radiation, 01β+

a. u⅔ → d-⅓ + 01β+

b. 11p → 10n + 01β+

2. 116C → 115B + 01β+

e. nuclide falls from high energy to low energy state

1. gamma radiation, 00γ—high penetration

2. matter-antimatter collision

a. 0-1e + 01e → γ

b. E = 2mec2

f. De Broglie wavelength: λparticle = h/p

6. artificial induced radioactivity (transmutation)

a. nuclide bombarded by subatomic particle (proton, neutron, alpha particle, etc.)

b. nuclear reaction

1. mass and charge are conserved

2. 10n + 147N → 146C + 11p

7. rate of decay and half-life

a. time it takes to reduce radioactivity by half is constant = half life, t½

b. 1 → 1/2 → 1/4 → 1/8 → 1/16 ...

B. Photons and Electrons

1. photon

a. quantum unit of electromagnetic energy

b. wave property, c = λf

1. wavelength, λ (m)

2. frequency, f (s-1)

c. energy, E = hf

[pic]

1. Planck's constant, h = 6.63 x 10-34 J•s

2. electromagnetic radiation

a. gamma > x-rays > UV > visible > IR > radio

b. violet > blue > green > yellow > orange > red

3. brightness measures intensity (not energy)

4. warm objects glow infrared (hot = visible light)

d. relativistic mass, m = E/c2

e. momentum, p = mc

f. interconnecting formulas

|Energy |E = mc2 |E = hf |E = hc/λ |E = pc |

|Momentum |p = mc |p = hf/c |p = h/λ |p = E/c |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

2. electron

a. electron properties

1. same charge as proton, but negative

2. smaller mass, 9.11 x 10-31 kg (0.00054858 u)

b. electron structure in an atom: Bohr model

[pic]

1. electrons occupy discrete energy levels

a. En = -B/n2 (BH = 13.6 eV)

b. n = energy level #

c. electron volt (eV) = small unit of energy

1 eV = 1.6 x 10-19 J

2. electrons change n by absorbing/emitting photons

a. Ephoton = En-high – En-low

b. EeV = 1240 eV•nm/λnm

c. photoelectrons

1. Ephoton > ionization energy ∴ atom emits electron

2. Einstein's photoelectric effect equation

[pic]

a. Kelectron = Ephoton – φ

|Kelectr| | |

|on | | |

| | | |

| | | |

| | | |

| | | |

| | | |

| |threshold fphoton |

b. φ called "work function" = ionization energy

1. minimum energy for photoelectrons

2. threshold λnm = 1240 eV•nm/φeV

c. electron can be stopped by a reverse voltage

1. called stop voltage, Vstop

2. Vstop = Kelectron (in eV)

3. (KeV)(1.6 x 10-19) = KJ

KJ = ½(9.11 x 10-31 kg)v2

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

A. Atomic Nucleus

Questions 1-21 Briefly explain your answer.

1. There are 82 protons in a lead nucleus. Why doesn't the lead nucleus burst apart?

(A) electric repulsive forces don't exist in the nucleus

(B) gravity overpowers the electric repulsion

(C) neutrons neutralize the positively charged protons

(D) none of the above

| |

2. What weighs more, A—an electron and a proton, or B—a hydrogen atom?

(A) A (B) B (C) tie

| |

Questions 3-5 radiation passes through a vacuum, where one side is positively charged and the other is negatively charged. ++++++++++++++++++++

A

B

_ _ _ _ _ _ _ _ _ _ _ _ _ _ C

3. Which is the path of an alpha particle?

| |

4. Which is the path of a beta particle?

| |

5. Which is the path of gamma radiation?

| |

Questions 6-9 Refer to the nonspontaneous nuclear decay:

23892U → 23490Th + 42He.

6. Which weighs more, A—U-238, or B—Th-234 + He-4?

(A) A (B) B (C) tie

| |

7. Which has greater momentum, A—Th-234, or B—He-4?

(A) A (B) B (C) tie

| |

8. Which has greater velocity, A—Th-234, or B—He-4?

(A) A (B) B (C) tie

| |

9. Which has greater kinetic energy, A—Th-234, or B—He-4?

(A) A (B) B (C) tie

| |

10. What is produced by the beta decay of 32H?

(A) 21H (B) 11H (C) 32He (D) 42He

| |

11. What is produced by the alpha decay of 21084Po?

(A) 21082Pb (B) 20682Pb (C) 21086Rn (D) 21486Rn

| |

12. Complete the nuclear equation: 146C + 0-1e → ___

(A) 156C (B) 157N (C) 145B (D) 147N

| |

13. Complete the nuclear equation: 10n + 168O → ___ + 21H

(A) 178O (B) 158O (C) 157N (D) 159F

| |

Questions 14-15 16 g of radioactive material has a 30-yr half-life.

14. How much is left after 90 years?

(A) 8 g (B) 4 g (C) 2 g (D) 1 g

| |

15. How long will it take to reduce the amount to 8 g?

(A) 30 yr (B) 60 yr (C) 90 yr (D) 120 yr

| |

16. What is the half life of a radioactive material that decays to ¼ the original amount in 16 years?

(A) 1 yr (B) 2 yr (C) 4 yr (D) 8 yr

| |

17. Which is more radioactive, substances A (t½ = 100 s) or B (t½ = 50 s)?

(A) A (B) B (C) tie

| |

18. Which type of radiation goes farther in matter before losing all of its energy?

(A) alpha (B) beta (C) gamma

| |

19. The speed of proton A is faster than proton B. Which one has the longer De Broglie wavelength?

(A) A (B) B (C) tie

| |

20. A proton and electron have the same speed, which has the longer De Broglie wavelength?

(A) proton (B) electron (C) tie

| |

21. A proton and neutron have the same speed, which has the longer De Broglie wavelength?

(A) proton (B) electron (C) tie

| |

22. Define

|nucleon | |

|nuclide | |

|Z # | |

|A # | |

|isotope | |

23. Consider a carbon-12 atom (a.m. = 12.0 u).

a. What is the mass in kg?

| |

b. What is the energy equivalence in J?

| |

24. Complete the following chart for the isotope, U-235.

|Number of |Number of |Number of |Z value |A value |

|nucleons |protons |neutrons | | |

| | | | | |

25. Consider the helium nuclide (42He = 4.001504). Determine

a. the difference in mass between nucleons and nuclide.

(1) in u

| |

(2) in kg

| |

b. the total binding energy in J.

| |

c. the binding energy per nucleon.

| |

26. Complete the following chart.

| |Symbol |Mass |Charge |Penetrating ability |

|alpha | | | | |

|beta | | | | |

|gamma | | | | |

27. Fill in the missing symbols.

|10B + n → α + ___ |___ + n → γ + 2H |50Cr + n → γ + ___ |

28. Consider the alpha decay of U-238: 238U → 4He + 234Th

|238U = 238.050784 u |4He = 4.002602 u |234Th = 234.055381 u |

a. Determine the change in mass per U-238 atom.

(1) in u

| |

(2) in kg

| |

b. Is the reaction spontaneous?

| |

c. Determine the change in energy (in J) per atom.

| |

29. A sample of 100Pd (half-life 4 days) has mass 1.776 g at 3:00 P.M. on July 4; what mass of 100Pd remains at 3:00 P.M. on July 16?

| |

30. Consider a helium-4 atom (atomic mass = 4.00 u).

a. What is the mass in kg?

| |

b. What is the energy equivalence in J?

| |

31. Complete the following chart for the isotope, Rn-226.

|Number of |Number of |Number of |Z value |A value |

|nucleons |protons |neutrons | | |

| | | | | |

32. Calculate the binding energy (in joules) of an average nucleon in 3H (3.015500 u).

| |

33. Fill in the missing symbols.

|27Al + α→ ___ + 30P |9Be + α → n + ___ |

34. Stationary Radium-226 (225.97709 u) undergoes an alpha decay (4.001504 u) to produce radon-222 (221.97036).

a. Write a nuclear equation for this radioactive decay.

| |

b. Calculate the change in mass in kg for this reaction.

| |

c. Calculate the energy is joules released per decay.

| |

d. If all the released energy becomes kinetic energy, what is Kα/KRa?

| |

e. If 98 % of the energy is absorbed by the alpha particle in

the form of kinetic energy. What is the particle's velocity?

| |

f. What is the De Broglie wavelength of the alpha particle?

| |

35. How long does it take for a sample of 32P (T1/2 = 14 days) to lose 7/8 of its activity?

| |

B. Photons and Electrons

36. Check which color has the greatest value for the following.

| |red |yellow |violet |can't tell |

|frequency | | | | |

|wavelength | | | | |

|energy | | | | |

|relativistic mass | | | | |

|momentum | | | | |

|intensity | | | | |

37. Complete the chart for an X-ray photon (λ = 1.54 x 10-10 m).

|f | |

|E | |

|m | |

|p | |

38. A proton and antiproton (m = 1.67 x 10-27 kg) collide and convert all mass into photon energy. Determine the photon's

|E | |

|f | |

|λ | |

|p | |

Questions 39-47 Briefly explain your answer.

39. What is the ionization energy of ground state hydrogen?

(A) 0 eV (B) 13.6 eV (C) 41.2 eV (D) 54.4 eV

| |

40. Which transition results in the greatest gain in energy?

(A) 2 → 5 (B) 5 → 2 (C) 3 → 10 (D) 1 → 2

| |

41. The Balmer series includes two blue, a blue-green and red spectral line. Which transition generates the red?

(A) 3 → 2 (B) 4 → 2 (C) 5 → 2 (D) 6 → 2

| |

42. A hydrogen electron is excited to n = 4. How many different transitions are possible to reach ground state?

(A) 1 (B) 2 (C) 3 (D) 6

| |

Question 43-45 Metal A has a greater work function φ compared to metal B.

43. Which metal has the greater threshold wavelength?

(A) A (B) B (C) tie

| |

44. Which metal has the greater threshold frequency?

(A) A (B) B (C) tie

| |

45. Yellow light does NOT generate photoelectrons in metal A. Which color(s) might be able to generate photoelectrons?

(A) red (B) orange (C) green (D) blue

| |

Questions 46-47 A metal surface emits photoelectrons when exposed to 400-nm light.

46. What will happen if the metal is exposed to 300-nm light?

(A) more electrons are emitted

(B) fewer electrons are emitted

(C) more energetic electrons are emitted

(D) no electrons are emitted

| |

47. What will happen if the metal is exposed to brighter 400-nm light?

(A) more electrons are emitted

(B) fewer electrons are emitted

(C) more energetic electrons are emitted

(D) no electrons are emitted

| |

48. The chart lists the energy levels for a hypothetical atom.

|Level (n) |1 |2 |3 |4 |5 |

|Energy (eV) |-14 |-10 |-5 |-3 |-1 |

a. Calculate the change in energy for each transition.

|En-low|En-high |

| |5 |4 |3 |2 |

|1 | | | | |

|2 | | | | |

|3 | | | | |

|4 | | | | |

b. Ground state atoms are irradiated with photons having a continuous range of energies between 7eV and 10 eV. What energies can be emitted by atoms of this gas?

| |

49. Complete the chart for a hydrogen transition from n = 3 → 1.

|E3 | |

|E1 | |

|E3 – E1 | |

|λphoton | |

50. What is the threshold wavelength that will emit electrons from a metal whose work function is 3.10 eV?

| |

51. A metal surface (φ = 2.40 eV) is exposed to 240 nm light.

a. What is the energy of the photons?

| |

b. What is the maximum kinetic energy (in eV) of electrons ejected from a surface?

| |

52. When 230-nm light falls on a metal, the photoelectrons are stopped with a voltage of 1.64 V.

a. What is the kinetic energy of the photoelectrons?

| |

b. What is the energy of the photons?

| |

c. What is the work function of the metal?

| |

53. Red light has a wavelength of 750 nm. Determine the

|f | |

|E | |

|m | |

|p | |

54. Consider an electron that transitions from the second energy level to ground state on a hydrogen atom.

a. What are E1 and E2?

| |

b. What is ΔE of the emission line?

| |

c. What is the wavelength of the photon?

| |

d. How much energy is needed to ionize an electron in the n = 2 state?

| |

55. A sodium surface (φ = 2.28 eV) is illuminated by 500 nm light.

a. What is the energy per photon?

| |

b. What is the maximum kinetic energy of the photoelectrons?

| |

c. What is the threshold wavelength for photoemission from the surface of sodium?

| |

d What is the kinetic energy of the photoelectrons when 600 nm light shines on the sodium surface?

| |

Practice Multiple Choice (No calculator)

Briefly explain why the answer is correct in the space provided.

1. The nuclear reaction X → Y + Z occurs spontaneously. If Mx, My, and Mz are the masses of the three particles, which of the following relationships is true?

(A) MX < MY – MZ (B) MX < MY + MZ

(C) MX > MY + MZ (D) MX – MY < MZ

| |

2. A negative beta particle is emitted during the radioactive decay of 21482Pb. Which is the resulting nucleus?

(A) 21080Hg (B) 21481Tl (C) 21383Bi (D) 21483Bi

| |

3. The deuteron (21H) mass md is related to the neutron mass mn and the proton mass mp by which of the following?

(A) md = mn + mp (B) md = mn + mp + mBE

(C) md = 2(mp) (D) md = mn + mp – mBE

| |

4. At noon the decay rate is 4,000 counts/minute. At 12:30 P.M. the decay rate is 2,000 counts/minute. The predicted decay rate in counts/minute at 1:30 P.M. is

(A) 0 (B) 500 (C) 667 (D) 1,000

| |

5. In the photoelectric effect, the maximum speed of electrons emitted by a metal surface when it is illuminated by light depends on which of the following?

I. Intensity of the light

II. Frequency of the light

III. Nature of the photoelectric surface

(A) I only (B) II only (C) III only (D) II and III only

| |

6. If photons of light of frequency f have momentum p, photons of light of frequency 2f will have a momentum of

(A) 2p (B) ½p (C) p (D) 4p

| |

7. Light of a particular wavelength is incident on a metal surface, and electrons are emitted from the surface as a result. To produce more electrons per unit time but with less kinetic energy per electron, one should

(A) Increase the intensity and decrease the wavelength.

(B) Increase the intensity and the wavelength.

(C) Decrease the intensity and the wavelength.

(D) Decrease the intensity and increase the wavelength.

| |

8. If the momentum of an electron doubles, its de Broglie wavelength is multiplied by a factor of

(A) ¼ (B) ½ (C) 1 (D) 2

| |

Questions 9-14 The diagram shows the energy levels for hydrogen gas.

[pic]

9. What is the energy, in eV, of a photon emitted by an electron as it moves from the n = 6 to the n = 2?

(A) 0.38 eV (B) 3.02 eV (C) 3.40 eV (D) 13.60 eV

| |

10. The energy of the photon (in J) is closest to

(A) 6.1 x 10-20 J (B) 4.8 x 10-19 J

(C) 5.4 x 10-19 J (D) 2.2 x 10-18 J

| |

11. What is the frequency of the emitted photon?

(A) 9.2 x 1013 s-1 (B) 7.3 x 1014 s-1

(C) 8.2 x 1014 s-1 (D) 3.3 x 1015 s-1

| |

12. What is the wavelength of the emitted photon?

(A) 4.1 x 10-7 m (B) 3.3 x 10-7 m

(C) 5.4 x 10-7 m (D) 5.0 x 10-7 m

| |

13. What is the minimum amount of energy needed to ionized an electron that is initially in the n = 6 energy level?

(A) 13.22 eV (B) 5.12 eV

(C) 0.38 eV (D) 0.16 eV

| |

14. A photon having energy of 9.4 eV strikes a hydrogen atom in the ground state. Why is the photon not absorbed by the hydrogen atom?

(A) The atom's orbital electron is moving too fast

(B) The photon striking the atom is moving too fast.

(C) The photon's energy is too small.

(D) The photon is being repelled by electrostatic force.

| |

15. Electrons with energy E have a de Broglie wavelength of approximately λ. In order to obtain electrons whose de Broglie wavelength is 2λ, what energy is required?

(A) ¼E (B) ½E (C) 2E (D) 4E

| |

Questions 16-18 Use the graphs to answer the questions.

(A) (B)

(C) (D)

16. Which graph shows the de Broglie wavelength of a particle versus the linear momentum?

| |

17. Which graph shows the maximum kinetic energy of the emitted electrons versus the frequency of the light?

| |

18. Which graph shows the total photoelectric current versus the intensity of the light for a fixed frequency above the cutoff frequency?

| |

Questions 19-20 The spectrum of visible light emitted during transitions in excited hydrogen atoms is composed of blue, green, red, and violet lines

19. What characteristic determines energy carried by a photon?

(A) amplitude (B) phase

(C) frequency (D) velocity

| |

20. Which color is associated with the greatest energy change?

(A) blue (B) red (C) green (D) violet

| |

Practice Free Response

1. The fusion of a proton (11p = 1.007276 u) and neutron

(10n = 1.008665 u) produces deuterium, 21H (2.013553 u).

a. Write a nuclear equation.

| |

b. Calculate the change in mass in atomic mass units, u.

| |

c. Calculate the change in mass in kg. (1 u = 1.66 x 10-27 kg)

| |

d. Calculate the energy in joules released.

| |

e. If the deuterium absorbs all of the energy from part d in the form of kinetic energy, what is the speed of the deuterium particle?

| |

2. Following a nuclear reaction, a nucleus of aluminum is at rest in an excited state represented by 2713Al* , as shown below left. The excited nucleus returns to the ground state 2713Al by emitting a gamma ray photon of energy 1.02 MeV (1.02 x 106 eV), as shown below right. The aluminum nucleus in the ground state has a mass of 4.48 x 10-26 kg.

[pic]

Determine

a. the energy of a photon in joules.

| |

b. the frequency of a photon.

| |

c. the wavelength of a photon.

| |

d. the momentum of a photon.

| |

e. the speed of the recoiling nucleus in m/s.

| |

f. the kinetic energy of the recoiling nucleus in joules.

| |

3. The diagram below shows the lowest four discrete energy levels of an atom. An electron in the n = 4 state makes a transition to the n = 2 state, emitting a photon of wavelength 121.9 nm.

[pic]

Determine

a. the energy level of the n = 4 state.

| |

b. the momentum of the photon.

| |

The photon is then incident on a silver surface in a photoelectric experiment, and the surface emits an electron with maximum possible kinetic energy. The work function of silver is 4.7 eV. Determine

c. the kinetic energy, in eV, of the emitted electron.

| |

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download