Q. The $K_{\alpha}\ X$-rays arising from a cobalt ($z = 27$) target have a wavelength of $179\ pm.$ The $K_{\alpha}\ X$-rays arising from a nickel target ($z = 28$) is

A) $> 179\ pm$
B) $< 179\ pm$
C) $= 179\ pm$
D) None of these
Explanation

(b) $\lambda_{k\alpha} \propto \frac{1}{(Z - 1)^{2}} \Rightarrow \frac{\lambda_{Ni}}{\lambda_{Co}} = \left( \frac{Z_{Co} - 1}{Z_{Ni} - 1} \right)^{2} = \left( \frac{27 - 1}{28 - 1} \right)^{2}$
$\Rightarrow \lambda_{Ni} = \left( \frac{26}{27} \right)^{2} \times \lambda_{Co} = \left( \frac{26}{27} \right)^{2} \times 179 = 165.9\ pm < 179pm$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.