Quantum Mechanics Problems and Questions

The Quantum

  1. Who first envisioned the concept of quantized light, and what problem was he trying to solve?
  2. Did Max Planck actually believe that light is composed of particles?
  3. Albert Einstein did not win his Nobel Prize for relativity theory. What did he win it for?
  4. Why does the frequency of light determine if an electron is ejected from a metal surface, not the brightness of the light?

1.00 eV = 1.60 x 10-19 J

h = 6.626 x 10-34 Js

  1. Gamma rays emitted during the explosion of a nuclear bomb have energy equal to1.92 x 10-13 J per photon. What is the frequency of this gamma ray emission? 2.90 x 1020 hz
  2. An X-ray technician always steps out of the room when the X-ray machine is on. How much energy in joules is carried by each photon of X-ray radiation if the wavelength is 0.0800 nm? 2.48 x 10-15 J
  3. In a helium-neon laser, excited helium atoms collide with neon atoms, raising the neon to an excited state where its energy is 20.7 eV. Stimulated emission then causes electrons in the neon to drop to a lower energy level where E = 18.7 eV. What is the wavelength and color of the light given off by a helium-neon laser? Hint: the energy of the photons is equal to the difference in the energy levels. 621 nm, red
  1. The work function for Hg = 4.50 eV. At what threshold frequency (when KE = 0) are electrons liberated from the surface of mercury? What portion of the electromagnetic spectrum corresponds to this frequency (find the wavelength). 276 nm, UV
  2. Albert shines violet light (415 nm) on a photocell that has a work function of 2.38 eV. What is the kinetic energy of photoelectrons released? 9.82 x 10-20 J
  3. Albert shines light from a He-Ne laser (633 nm) on the same photocell. Does the red laser light eject electrons?

Waves and Particles

  1. Light does not have mass, but it does possess momentum. Whose experiment showed this and how?
  2. According to Louis deBroglie, what two wave-properties should an electron (a particle) possess?
  1. What is the momentum of a 0.80 nm x-ray photon? 8.3 x 10-25 kgm/s
  2. What is the frequency and energy of a photon with a momentum of 4.25 x 10-26 kgm/s?

1.92 x 1016 hz, 1.28 x 10-17 J

  1. How many photons of He-Ne laser light (633 nm) would have the same momentum as a 0.1 kg mass moving at 0.25 m/s? (hint: first find the momentum of the mass, next find the total momentum of the light, and then determine the momentum of each photon) 2.38 x 1025 photons
  1. At Bell Labs in 1926, Davisson and Germer aimed a beam of electrons (mass = 9.11 x 10-31 kg) at a nickel crystal whose atomic spacing was 2.15 Angstroms (2.15 x 10-10 m). If the electrons had a speed of 4.4 x 106 m/s, calculate the de Broglie wavelength of the electrons to determine whether they would be able to pass through the crystalline structure (or be reflected back). In order to pass through, the electrons must have a wavelength smaller than the spacing. yes, 1.65 x 10-10 m < 2.15 x 10-10 m
  2. What is the de Broglie wavelength of a 0.0125 kg bullet fired from a rifle at 495 m/s? Is there any chance that the bullet would diffract around you? The bullet must have a wavelength wider than you in order to diffract.

no way,  = 1.1 x 10-34 m

The Bohr Atom

  1. Why can electrons only exist in specific energy levels? (consider a wave-property of electrons)
  2. In order to determine the orbital radii of electrons in hydrogen, Bohr had to set what two equations equal to one another?
  3. What kind of radiation would be emitted by a hydrogen atom if an electron drops from a higher energy level (n = 2, 3, 4…) to the first energy level (n = 1)?
  4. Why didn’t Bohr calculate the allowable orbital radii of elements other than hydrogen (like He, Li, and so on)?

r = n2 (h2/4p2Kq2m) = n2(53pm)En = –2pK2mq4/h2n2=–13.6 eV · (1/n2)Ephoton = Ef – Ei

  1. What is the orbital radius of an electron in the second energy level of a hydrogen atom?
  2. How much energy is needed to make an electron make a quantum leap from n = 2 to n = 5 in a hydrogen atom? Calculate in both eV and J.
  3. What is the wavelength and color of the photon in the previous problem?

Uncertaintyand Probability

  1. What is so strange about the double-slit experiment when photons enter the double slit individually?
  2. What is the Heisenberg uncertainty principle and how does it affect the study of subatomic particles?
  3. Using the Heisenberg uncertainty principle, explain why gamma rays act more like particles than like waves.
  4. What is an electron orbital and whose equation is used to determine the shape of an orbital? What does the shape really represent?