Question

$K_{\alpha }$ wavelength emitted by an atom of atomic number $Z=11$ is $\lambda $ . Find the atomic number for an atom that emits $K_{\alpha }$ radiation with wavelength $4\lambda $ .

• A. $Z=6$
• B. $Z=4$
• C. $Z=11$
• D. $Z=44$

Answer 1

Answer: (A)

$\frac{1}{\lambda} \propto( Z -1)^2 $
$\therefore \frac{\lambda_1}{\lambda_2}=\frac{\left( z _2-1\right)^2}{\left( z_1-1\right)^2}$
$\frac{1}{4}=\left(\frac{ Z _2-1}{11-1}\right)^2$
Solving this, we get, $Z_2=6$