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- 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?

- 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 which will just ionize
the atom.

- The maximum energy of photoelectrons from aluminium is 2.3 eV
for radiation of wavelength , and 0.90 eV for radiation of
wavelength . Use this data to calculate Planck's constant,
and the work function of aluminium.

- Show that the de Broglie wavelength of an electron accelerated from rest across a potential difference
is given by

where is measured in volts.

- 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.

- 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 ?

- 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.

- 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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Richard Fitzpatrick
2010-07-20