Question

Find the

(a) maximum frequency

(b) Minimum wavelength of X-rays produced by 30 kV electrons.

Answer 1

(a). Potential of the electrons, $V=30kV=3\times {10}^{4}V$

Hence, energy of the electrons, $E=3\times {10}^{4}eV$

Where,

e = Charge on an electron = $1.6\times {10}^{-19}C$

Maximum frequency produced by the X-rays is $\nu$

The energy of the electrons is given by the relation is $E=h\nu$

Where,

h = Planck’s constant = $6.626\times {10}^{-34}Js$

$\nu =E/h=7.24\times {10}^{18}Hz$

(b). Energy of a electron, $E=30\times {10}^{3}eV$

Let Maximum frequency produced by the X-rays be $\nu$

$\nu =E/h=1.6\times {10}^{-19}\times 3\times {10}^4/6.626\times {10}^{-34}=7.24\times {10}^{18}Hz$ where $h$ is the planck's constant.

The minimum wavelength produced by the X-rays is given as-

$\lambda =c/\nu =0.0414nm$