X-Ray Production by Fast Electrons When a fast electron (i.e., one moving at a r
ID: 2019138 • Letter: X
Question
X-Ray Production by Fast Electrons
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= K - K"
where K and K' are the kinetic energies of the electron before and after radiation, respectively.
This kind of radiation is called bremsstrahlung radiation, which in German means "braking radiation" or "deceleration radiation." The highest energy of a radiated photon corresponds to the moment when the electron is completely stopped.
Question:
Given an electron beam whose electrons have kinetic energy of 7.00 keV , what is the minimum wavelength wavelength min of light radiated by such beam directed head-on into a lead wall?
Express your answer numerically in nanometers.
Answer I tried was 1.77*10^-11 and it was wrong
Explanation / Answer
Knowns & unknowns :Planck's constant = h=6.625x10-34Js velocity of light c =3x 108 m/s Kinetic energy of electrons : K = 7 Ke V = 7 x ( 1.6x10-16 ) J = 11.2 x10-16 J Minimum wavelength is given by the formual min = ch / K min = (3 x 108 )(6.625 x 10-34 ) / (11.2 x10-16 ) = 1.774x10-10 m or 1.774 oA = 1.774x10-10 m or 1.774 oA
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