Question:
Find the:
(a) Maximum frequency, and
(b) The minimum wavelength of X-rays produced by 30 kV electrons.
Solution:
Electron potential, V = 30 kV = 3 × 104 V
Hence, electron energy, E = 3 × 104 eV
Where, e = Charge on one electron = 1.6 × 10-19 C
(a) Maximum frequency by the X-rays = ν
The energy of the electrons:
E = hν
Where,
h = Planck’s constant = 6.626 × 10-34 Js
Therefore, $v=\frac{E}{h}$
$=\frac{1.6 \times 10^{-19} \times 3 \times 10^{4}}{6.626 \times 10^{-34}}=7.24 \times 10^{18} \mathrm{~Hz}$
Hence, 7.24 x 1018 Hz is the maximum frequency of the X-rays.
(b) The minimum wavelength produced:
$\lambda=\frac{c}{v}$
$=\frac{3 \times 10^{8}}{7.24 \times 10^{18}}=4.14 \times 10^{-11} \mathrm{~m}=0.0414 \mathrm{~nm}$