According to Moseley's law, $\sqrt{
u} = a(Z - b)$ for the characteri…

Question

According to Moseley's law, $\sqrt{
u} = a(Z - b)$ for the characteristic X-ray lines. If two elements emit $K_\alpha$ X-rays with frequencies in the ratio $
u_1 : 
u_2 = 4 : 9$, then their atomic numbers (ignoring screening $b$) satisfy

Accepted Answer

A. $Z_1 : Z_2 = 2 : 3$

From $\sqrt{
u} \propto Z$ (taking $b=0$ for ratio purposes), $	frac{Z_1}{Z_2} = 	frac{\sqrt{
u_1}}{\sqrt{
u_2}} = 	frac{\sqrt{4}}{\sqrt{9}} = 	frac{2}{3}$.

Answer

$Z_1 : Z_2 = 4 : 9$

Answer

$Z_1 : Z_2 = 3 : 2$

Answer

$Z_1 : Z_2 = \sqrt{2} : \sqrt{3}$

According to Moseley's law, $\sqrt{\nu} = a(Z - b)$ for the characteristic X-ray lines. If two elements emit $K_\alpha$ X-rays with frequencies in the ratio $\nu_1 : \nu_2 = 4 : 9$, then their atomic numbers (ignoring screening $b$) satisfy