Question

The K_α and K_β X-rays of molybdenum have wavelengths 0.71 A and 0.63 A respectively. Find the wavelength of L_α X-ray of molybdenum.

Answer 1

Given:
Wavelength of K_α X-rays, $\lambda$₁ = 0.71 A
Wavelength of K_β X-rays, ${\lambda }_2$ = 0.63 A

For L_a X-ray of molybdenum,
a = 57
b = 1
From Moseley's equation,
$\sqrt{v}=a(\mathrm{Z}-b)$
Here, v = frequency of X-ray
Z = atomic number of the element
$$\begin{gathered} \sqrt{v}=a(\mathrm{Z}-b) \\ \Rightarrow \sqrt{v}=a(57-1) \\ =a\times 56...\left(1\right) \\ \mathrm{For}\mathrm{C}u\left(29\right), \\ \sqrt{1.88\times {10}^{18}}=a(29-1)=28a...\left(2\right) \end{gathered}$$
Dividing (1) and (2)
$$\begin{gathered} \sqrt{\frac{v}{1.88\times {10}^{18}}}=\frac{a\times 56}{a\times 28}=2 \\ \Rightarrow v=1.88\times {10}^{18}\times (2{)}^2 \\ =4\times 1.88\times {10}^{18} \\ =7.52\times {10}^{18}\mathrm{Hz} \end{gathered}$$