Question

Wavelength of $K_{\alpha }$ X-rays of two metals $A$ and $B$ are $\frac{4}{1875R}$ and $\frac{1}{675R}$ respectively, where $R$ is rydberg constant then [Take $b=1$]

• A. Number of elements lying between A and B according to atomic numbers is 4
• B. $Z_A=30$
• C. $Z_B=27$
• D. $Z_A=26$

Answer 1

Answer: (A), (D)

The correct options are
A Number of elements lying between A and B according to atomic numbers is 4
D $Z_A=26$

$\sqrt{\frac{c}{\lambda }}=\sqrt{\frac{3}{4}RC}(Z-b)$

For A $\Rightarrow \sqrt{\frac{1875}{3}}=(Z_A-b)\Rightarrow Z_A-b=25\dots \left(1\right)$

For B $\sqrt{\frac{675\times 4}{3}}=(Z_B-b)\Rightarrow Z_B-b=30\dots \left(2\right)$

By (1) and (2),

$\Rightarrow Z_A=26$ and $Z_B=31$