Q. $K_{\alpha}$ 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
Explanation
(a) $\ \ \ \ \ \ \ \ \ \ \frac{1}{\lambda}\ \propto (Z - 1)^{2}$
$\therefore\ \ \ \ \ \ \frac{\lambda_{1}}{\lambda_{2}} = \left( \frac{Z_{2} - 1}{Z_{1} - 1} \right)^{2}$
or $\frac{1}{4} = \left( \frac{Z_{2} - 1}{11 - 1} \right)^{2}$
Solving this we get, $Z_{2} = 6$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.