Question

The $K_{a}X-$rays of aluminium $(Z=13)$ and zinc $(Z=30)$ have wavelength $887pm$ and $146pm$ respectively. Use Moseley's law $\sqrt{v}=a(Z-b)$ to find the wavelength of the $K_{a}X-$ray of iron $(Z=26)$

Answer 1

Wavelength of K_a x-rays of Al

${\lambda }_1=887pm$

$V_a=\frac{c}{\lambda }$

$V_a=\frac{3\times {10}^8}{887\times {10}^{-12}}$

$=33.82\times {10}^{16}Hz$

For zinc

${\lambda }_2=146pm$

$v_z=\frac{3\times {10}^8}{146\times {10}^{-12}}$

$v_z=2.055\times {10}^{18}Hz$

According to Moseley’s law

$\sqrt{v}=a(Z-b)$

For Aluminium:

$5.815\times {10}^8=a(30-b)....................\left(1\right)$

for Zinc:

$1.4331\times {10}^9=a(30-b)...................\left(2\right)$

Dividing (1) by (2) we get

$\frac{13-b}{30-b}=\frac{5.815\times 10-1}{1.4331}$

$Onsolving,$

$b=1.3949$

$\&a=5\times {10}^7$

$forFe$

${\nu }^{\prime }=5\times {10}^7(26-1.39)$

$=123.05\times {10}^7$