The wavelength of -characteristic X-rays produced is , when cathode rays strike on a metal of atomic — Atomic Structure Chemistry Question

💡 Solution & Explanation

According to Moseley's Law, $\frac{1}{\lambda} \propto (Z-1)^2$. For a wavelength of $4\lambda$, we have $\frac{1}{4\lambda} \propto (Z'-1)^2$. Taking the ratio, $\frac{1}{4} = \frac{(Z'-1)^2}{(Z-1)^2} \implies \frac{1}{2} = \frac{Z'-1}{Z-1} \implies Z-1 = 2Z' - 2 \implies 2Z' = Z+1 \implies Z' = \frac{Z+1}{2}$. Therefore, correct answer is C.