2.13: Exercises

1. A He-Ne laser emits radiation of wavelength nm. How many photons are emitted per second by a laser with a power of 1 mW? What force does such laser exert on a body which completely absorbs its radiation?
2. The ionization energy of a hydrogen atom in its ground state is eV (1 eV is the energy acquired by an electron accelerated through a potential difference of 1 V). Calculate the frequency, wavelength, and wavenumber of the electromagnetic radiation that will just ionize the atom.
3. The maximum energy of photoelectrons from aluminium is 2.3 eV for radiation of wavelength 2000,Angstorm), and 0.90 eV for radiation of wavelength 2580 Angstrom. Use this data to calculate Planck’s constant, as well as the work function of aluminium.
4. Show that the de Broglie wavelength of an electron accelerated from rest across a potential difference is given by where is measured in volts.
5. If the atoms in a regular crystal are separated by demonstrate that an accelerating voltage of about would be required to produce an electron diffraction pattern from the crystal.
6. The relationship between wavelength and frequency for electromagnetic waves in a waveguide is where is the velocity of light in vacuum. What are the group- and phase-velocities of such waves as functions of and ?
7. Nuclei, typically of size m, frequently emit electrons with energies of 1–10 MeV. Use the uncertainty principle to show that electrons of energy 1 MeV could not be contained in the nucleus before the decay.
8. A particle of mass has a wavefunction where and are positive real constants. For what potential function does satisfy the Schrödinger equation?

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1. Plural of quantum: Latin neuter of quantus: how much?↩

Contributors and Attributions

• Richard Fitzpatrick (Professor of Physics, The University of Texas at Austin)