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Question

There is a vacancy in the L shell. Which of these transitions are possible?
  1. All of them.


Solution

The correct options are
B
C
So we have an electronic vacancy created in L-shell. Now let's think about each cases one by one. We just have to keep in mind that every system acts in a way to minimize its energy. No process is spontaneously possible in which the energy of the system increases. Only those transition/s will be possible after which the energy of the atom decreases.
From the atomic energy level diagram we know that the atomic energy is highest when there is a vacancy in K-shell and decreases further. i.e.  
EKELEMENAnd so on.
  
If a transition from K-shell occurs, the vacancy will shift to K-shell.  The atomic energy increase hence. So, this is not possible.
If a transition from M-shell happens, the atomic energy decreases, hence such a transition is possible.
Infact any transition in which the electron is jumping from a shell above L-shell to fill a vacancy here is possible.
 

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