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Im having trouble grasping the following problem:

Calculate the binding energy in the L-shell for copper, if the binding energy for the K-shell is $ \ 1,439*10^{-15} J\ $.

I know that you find the answer by first finding out the energy emitted by the $ K_{\alpha} $ and then using the following equation:

$${\frac{hc}{\lambda_L}=\frac{hc}{\lambda_K}-\frac{hc}{\lambda_K{\alpha}}} $$

So im not really out after the answer to the problem. Im out after understanding why the binding energy in the L-shell is equal to the binding energy in the K-shell minus the $K_{\alpha}$ emission.

Shouldn't the binding energy in the L-shell be equal to binding energy in the K-shell PLUS the $K_{\alpha}$ emission thus making the following equation instead:

$${\frac{hc}{\lambda_L}=\frac{hc}{\lambda_K}+\frac{hc}{\lambda_K{\alpha}}} ~?$$

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