Fast Electrons?

Question

INTRO:

When a fast electron (i.e., one moving at a relativistic speed) passes by a heavy atom, it interacts with the atom's electric field. As a result, the electron's kinetic energy is reduced; the electron slows down. In the meantime, a photon of light is emitted. The kinetic energy lost by the electron equals the energy E gamma of a photon of radiated light:

E gamma = K - K',

where K and K' are the kinetic energies of the electron before and after radiation, respectively.

QUESTION:

Given an electron beam whose electrons have kinetic energy of 9.00 keV, what is the minimum wavelength lambda min of light radiated by such beam directed head-on into a lead wall?

= ____ A

Answer 1

To find the minimum wavelength (or maximum energy) the electron must give up ALL of its energy. Therefore,

E (gamma) = KE ( electron ) = 9.00 keV.

The energy of a photon is equal to hc / λ where λ is the wavelength, c the speed of light, and h is Planck's constant. Plug in the energy (either convert to Joules or use Planck's Constant with units of eV-s) and solve for the wavelength.