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Physics 1220 In-Class Problems: Modern Physics

  1. It requires 13.6 eV to ionize a hydrogen atom. What wavelength of light would we need to do this? (1 eV = 1.602 × 10-19 J)

  2. In order to break a chemical bond in the molecules of human skin, causing sunburn, a photon of energy of about 3.5 eV is required. To what wavelength does this correspond?

  3. Electrons with maximum KE of 3.0 eV are ejected from a metal surface by ultraviolet radiation of wavelength 150 nm. Determine the work function and the corresponding threshold wavelength of the metal.

  4. An electron is accelerated through a potential difference of 20000 Volts. It then collides with a metal target. What is the minimum wavelength that an emitted photon can have?

  5. What wavelength must electromagnetic radiation have if the photon is to have the same momentum as an electron moving with speed 2.0 × 105 m/s. The mass of an electron is 9.1 × 10-31 kg.

  6. What is the maximum energy that a free electron (initially stationary) can acquire in a collision with a photon of energy 4.0 × 103 eV?

  7. A photon of initial wavelength 0.0400 nm suffers two successive collisions with two electrons. The deflection in the first collision is 90° and in the second collision is 60°. What is the is the final wavelength of the photon?

  8. What must be the energy of an electron if its wavelength is to equal the wavelength of visible light about 550 nm? (E = p2/2m , me = 9.11 × 10-31 kg)

  9. A photon and an electron each have an energy of 6.0 × 103 eV. What are their wavelengths?

  10. Suppose that the velocity of an electron has been measured to within an uncertainty of ±1 cm/s. What minimum uncertainty in the position of the electron does this imply?

  11. If the position of an automobile of mass 2 × 103 kg is uncertain by ±10-18 m, what is the corresponding uncertainty in its velocity?

  12. What are the orbital radii and electron velocities in the first three levels of the Bohr model of the hydrogen atom. (1/4pe0 = 8.99 × 109 N-m/C2, e = 1.602 × 10-19 C)

  13. Show for an ionized atom of charge Ze with only a single electron that the radius, speed, and energy of the electron in the nth orbit are: r = n2a0/Z, v = Ze2/(n4pe0), En = (-13.6 eV)Z2/n2. Note that the spectra for such an atom would have the same pattern as hydrogen but shifted in wavelength by Z2.

  14. When a block of metal serving as a target in an X-ray tube is bombarded with a beam of fast electrons, it emits X-rays of wavelength 0.167 nm. Assuming that these X-rays arise in transitions from the first excited state to the ground state, identify the metal.

  15. How far away can you see a 100-W light bulb at night? Assume that the light emitted has a wavelength of 550 nm and the threshold for your eye to detect light is 25 photons per second passing through your pupil. The diameter of a dark-adapted pupil is about 8 mm.

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