Question

The short wavelength limit of the X–rays produced, through the ‘complete coversion’ of the energy of a beam of electrons, accelerated through a potential, V, is 0.4125 Å. Taking h = 6.6 x 10^-34 J–s. The value of V, and the deBroglie wavelength, associated with a beam of electrons, accelerated through a potential of V volts, are (nearly) equal, respectively, to

(1) 30 kV and 0.7 Å

(2) 30 kV and 0.07 Å

(3) 3 kV and 0.007 nm

(4) 3 kV and 0.7 nm

Answer 1

(2) 30 kV and 0.07 Å

The energy of the accelerated beam of electrons = eV. When this energy is completely converted into X–rays of wavelength 0.4125Å , we have

The corresponding deBroglie wavelength is