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Quantum theory practice

QCE Physics · Original practice questions with worked solutions

All quantum theory practice questions

56 original questions · Page 2 of 3

  1. Q134 · Original practice · 7 marks
    Electrons accelerated through 150 V150\,\mathrm{V} strike a crystal. Assume non-relativistic motion.
    Quantum theory
  2. Q139 · Original practice · 6 marks
    For hydrogen, En=−13.6 eVn2E_n=-\frac{13.6\,\mathrm{eV}}{n^{2}}. An atom emits a photon in the transition n=5n=5 to n=2n=2.
    Quantum theory
  3. Q144 · Original practice · 11 marks
    In the Bohr model of the hydrogen atom, a single electron moves at constant speed vv in a circular orbit of radius rr around a stationary proton. The electric force between the proton and the electron provides the centripetal force.
    In the nnth allowed orbit, the angular momentum of the electron satisfies
    mvr=nh2πmvr = \frac{nh}{2\pi}
    where mm is the mass…
    Quantum theory
  4. Q152 · Original practice · 1 mark
    Monochromatic light has frequency below a clean metal's threshold frequency. Its intensity is increased tenfold while frequency remains constant. Within the usual one-photon photoelectric model, what occurs?
    Quantum theory
  5. Q182 · Original practice · 6 marks
    The graph shows two black-body spectra, each normalised separately so its own peak equals one. Their peak wavelengths are 966 nm966\,\mathrm{nm} for A and 483 nm483\,\mathrm{nm} for B. Use b=2.898×10−3 m Kb=2.898\times10^{-3}\,\mathrm{m\,K}.
    Quantum theory
  6. Q183 · Original practice · 6 marks
    The graph shows maximum photoelectron kinetic energy for metals M and N. Line M passes through (6.00×1014 Hz,1.3252×10−19 J)(6.00\times10^{14}\,\mathrm{Hz},1.3252\times10^{-19}\,\mathrm J) and (9.00×1014 Hz,3.3130×10−19 J)(9.00\times10^{14}\,\mathrm{Hz},3.3130\times10^{-19}\,\mathrm J). The frequency intercept of N is 6.00×1014 Hz6.00\times10^{14}\,\mathrm{Hz}. Assume straight-line fits.
    Quantum theory
  7. Q184 · Original practice · 7 marks
    A clean metal has work function 2.60×10−19 J2.60\times10^{-19}\,\mathrm J. It is illuminated at frequency 5.50×1014 Hz5.50\times10^{14}\,\mathrm{Hz}. Use h=6.626×10−34 J sh=6.626\times10^{-34}\,\mathrm{J\,s}, me=9.1093835×10−31 kgm_e=9.1093835\times10^{-31}\,\mathrm{kg} and c=3.00×108 m s−1c=3.00\times10^8\,\mathrm{m\,s^{-1}}. Assume one-photon emission.
    Quantum theory
  8. Q185 · Original practice · 7 marks
    An idealised atom has bound energy levels −8.00-8.00, −3.00-3.00 and −1.00 eV-1.00\,\mathrm{eV}, with ionisation at 0 eV0\,\mathrm{eV}. Its electron initially occupies the ground level. Incident photons have energies 4.004.00, 5.005.00, 7.007.00 or 8.50 eV8.50\,\mathrm{eV}. Ignore recoil and multi-photon processes. Use h=6.626×10−34 J sh=6.626\times10^{-34}\,\mathrm{J\,s},…
    Quantum theory
  9. Q186 · Original practice · 7 marks
    A hydrogen atom emits a photon as its electron falls from ni=5n_i=5 to nf=2n_f=2. Use R=1.097×107 m−1R=1.097\times10^7\,\mathrm{m^{-1}}. A second hydrogen photon has wavelength 1.282×10−6 m1.282\times10^{-6}\,\mathrm m and also begins from ni=5n_i=5.
    Quantum theory
  10. Q187 · Original practice · 7 marks
    In the Bohr standing-wave model, an electron occupies an n=3n=3 orbit of radius 4.76×10−10 m4.76\times10^{-10}\,\mathrm m. Use h=6.626×10−34 J sh=6.626\times10^{-34}\,\mathrm{J\,s} and me=9.1093835×10−31 kgm_e=9.1093835\times10^{-31}\,\mathrm{kg}. Treat the electron momentum as nonrelativistic.
    Quantum theory
  11. Q188 · Original practice · 7 marks
    Two observations are made: (1) monochromatic light passing through two narrow slits forms alternating bright and dark bands; (2) a metal shows a threshold frequency for immediate photoelectron emission, and no emission below threshold in the one-photon regime even at higher intensity.
    Quantum theory
  12. Q215 · Original practice · 1 mark
    Two black bodies have peak wavelengths 600 nm600\,\mathrm{nm} and 1200 nm1200\,\mathrm{nm}. What is the temperature of the first divided by the temperature of the second?
    Quantum theory
  13. Q216 · Original practice · 1 mark
    A monochromatic beam has fixed power PP, and its photons each have energy hfhf. Its frequency is doubled while its power stays fixed. What happens to the number of photons arriving per second?
    Quantum theory
  14. Q217 · Original practice · 1 mark
    A metal has threshold frequency f0f_0. The incident light frequency changes from 1.50f01.50f_0 to 2.00f02.00f_0. What is the new maximum photoelectron kinetic energy divided by its original value?
    Quantum theory
  15. Q218 · Original practice · 1 mark
    The diagram shows four bound energy levels of an atom. An electron starts at the lowest level. Which photon energy cannot excite it to one of the other three shown bound levels? Ignore broadening and multiphoton processes.
    Quantum theory
  16. Q219 · Original practice · 1 mark
    A non-relativistic electron beam's kinetic energy is increased by a factor of four. How does its de Broglie wavelength change?
    Quantum theory
  17. Q220 · Original practice · 1 mark
    In a thin-foil scattering experiment, most positively charged alpha particles pass through, but a small fraction deflect through very large angles. Which conclusion best accounts for both observations?
    Quantum theory
  18. Q239 · Original practice · 6 marks
    A photoelectric experiment plots maximum kinetic energy against 1/λ1/\lambda. The exact fitted line passes through A: (2.00×106 m−1,1.50×10−19 J)(2.00\times10^6\,\mathrm{m^{-1}},1.50\times10^{-19}\,\mathrm J) and B: (4.00×106 m−1,5.50×10−19 J)(4.00\times10^6\,\mathrm{m^{-1}},5.50\times10^{-19}\,\mathrm J). Use c=3.00×108 m s−1c=3.00\times10^8\,\mathrm{m\,s^{-1}}.
    Quantum theory
  19. Q240 · Original practice · 5 marks
    Two metals have work functions WA=2.00×10−19 JW_A=2.00\times10^{-19}\,\mathrm J and WB=3.00×10−19 JW_B=3.00\times10^{-19}\,\mathrm J. A monochromatic beam must produce a maximum photoelectron kinetic energy of at least 1.00×10−19 J1.00\times10^{-19}\,\mathrm J from each metal. Use h=6.626×10−34 J sh=6.626\times10^{-34}\,\mathrm{J\,s} and c=3.00×108 m s−1c=3.00\times10^8\,\mathrm{m\,s^{-1}}.
    Quantum theory
  20. Q241 · Original practice · 6 marks
    An atom has the bound energy levels shown. An electron initially in the ground state absorbs one photon and reaches the highest shown level. It then returns to the ground state in exactly two radiative steps. The first emitted photon has energy 6.00 eV6.00\,\mathrm{eV}. Use h=6.626×10−34 J sh=6.626\times10^{-34}\,\mathrm{J\,s}, c=3.00×108 m s−1c=3.00\times10^8\,\mathrm{m\,s^{-1}} and…
    Quantum theory
  21. Q242 · Original practice · 5 marks
    An electron beam and a proton beam both have de Broglie wavelength 2.00×10−10 m2.00\times10^{-10}\,\mathrm m. Both are non-relativistic. Use h=6.626×10−34 J sh=6.626\times10^{-34}\,\mathrm{J\,s}, me=9.1093835×10−31 kgm_e=9.1093835\times10^{-31}\,\mathrm{kg} and mp=1.6726219×10−27 kgm_p=1.6726219\times10^{-27}\,\mathrm{kg}.
    Quantum theory
  22. Q269 · Original practice · 4 marks
    The axes show the spectral radiance per unit wavelength of a black body at 3000 K3000\,\mathrm K. On these same axes, sketch the curve for the same source at 4500 K4500\,\mathrm K. The curves are not separately normalised. Use b=2.898×10−3 m Kb=2.898\times10^{-3}\,\mathrm{m\,K}.
    Quantum theory
  23. Q270 · Original practice · 3 marks
    A student models a heated cavity using a classical model that lets each electromagnetic mode exchange energy continuously. It predicts an unbounded increase in emitted energy at very short wavelengths, unlike the observed finite spectrum.
    Quantum theory
  24. Q271 · Original practice · 3 marks
    Rutherford extquotesingle s model places a small positive nucleus at the centre of the atom with electrons outside it. Consider an electron modelled as orbiting classically.
    Quantum theory