Question

Let $v_{K_{\alpha }}$, $v_{K_{\beta }}$, and $v_{L_{\alpha }}$ are the frequencies of $K_{\alpha }$, $K_{\beta }$ and $L_{\alpha }$. X-raylines of a material, then

• A. $v_{K_{\alpha }}$ + $v_{K_{\beta }}$ = $v_{L_{\alpha }}$
• B. $v_{K_{\alpha }}$ - $v_{K_{\beta }}$ = $v_{L_{\alpha }}$
• C. $v_{L_{\alpha }}$ + $v_{K_{\alpha }}$ = $v_{K_{\beta }}$
• D. $v_{K_{\alpha }}$ - $v_{L_{\alpha }}$ = $v_{K_{\beta }}$

Answer 1

The correct option is C $v_{L_{\alpha }}$ + $v_{K_{\alpha }}$ = $v_{K_{\beta }}$

The $K_{\alpha }$ wavelength is emitted when the atom transitions from $K$ energy state to the $L$ energy state. The $K_{\beta }$ wavelength is emitted when the atom transitions from $K$ energy state to the $M$ energy state. The $L_{\alpha }$ wavelength is emitted when the atom transitions from $L$ energy state to the $M$ energy state. So balancing energies, Energy released in $K_{\beta }$ emission is equal to sum of those released in $K_{\alpha }$ and $L_{\alpha }$ emissions. and, $frequency\propto energyreleased$

So, $v_{K_{\beta }}=v_{L_{\alpha }}+v_{K_{\alpha }}$