Dual Nature of Radiation and Matter — Physics STD 12 Science — Question

1. Maximum frequency produced by the X-rays = v

The energy of the electrons is given by the relation:

E = hv

Where,

h = Planck's constant = 6.626 × 10-34 Js

$\therefore\ \text{v}=\frac{\text{E}}{\text{h}}$

$=\frac{1.6\times10^{-19}\times3\times10^4}{6.626\times10^{-34}}=7.24\times10^{18}\ \text{Hz}$

Hence, the maximum frequency of X-rays produced is 7.24 × 10¹⁸ Hz.

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

$\lambda=\frac{\text{c}}{\text{v}}$

$=\frac{3\times10^{8}}{7.24\times10^{18}}=4.14\times10^{-11}\ \text{m}=0.0414\ \text{nm}$

Hence, the minimum wavelength of X-rays produced is 0.0414 nm.