Which transition is not possible? 

Concept:

Selection Rules for Electronic Transitions: In atomic transitions, certain rules known as selection rules govern which electronic transitions are allowed or forbidden. These include:

• Total Angular Momentum Selection Rule: The change in the total angular momentum quantum number(\( j \)) must be \(Δ j =0, \pm 1\).
• Angular Momentum (Orbital) Selection Rule: The change in the orbital angular momentum quantum number(\(l\)) must be \(Δ l = \pm 1\) .
• Spin Selection Rule: The spin quantum number must not change during the transition. i.e. \(Δ s = 0\) .

Explanation:

Let us check options one by one:

1.  2F5/2 → 2D5/2

\(Δj=(5/2-5/2)=0\\ Δl=(3-4)=-1\\ Δs=(1/2-1/2)=0\)

Possible.

2.   2D3/2 → 2P1/2

\(Δj=(1/2-3/2)=-1\\ Δl=(2-3)=-1\\ Δs=(1/2-1/2)=0\)

Possible.

3.   2D3/2 → 2S1/2

\(Δj=(1/2-3/2)=-1\\ Δl=(1-3)= -2\\ Δs=(1/2-1/2)=0\)

Not possible.

4.  2P1/2 → 2S1/2

\(Δj=(1/2-1/2)=0\\ Δl=(1-2)=-1\\ Δs=(1/2-1/2)=0\)

Possible.

The correct answer is option 3.