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Question

Compare the energy released during direct electronic transition from 4th orbit to 1st orbit with the energy released during successive electronic transitions between the same orbits in H-atom. Is the energy of all successive transitions between the 4th orbit and 1st orbit equal?


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Solution

  1. When an electron moves from one orbit to another in a hydrogen atom, the energy released is calculated as follows:

E=-13.61n22-1n12eV

2. The energy released during direct electronic transition from 4th orbit to 1st orbit;

E=-13.61122-1412eVE=12.75eV

3. Now, the energy is released when the successive electronic transitions between the fourth orbit to the first orbit occur.

( successive transition means electron jumps from 4321)

4. Consider; E1,E2,E3 are the energies released when the electron jumps from 4321respectively.

E1=-13.6132-142eVE1=-0.66eV

E2=-13.6122-132eVE2=-1.89eV

E3=-13.6112-122eVE3=-10.2eV

5. Now, E1+E2+E3=-0.66eV-1.89eV-10.2eV=-12.75eV

6. This is the amount of energy released during the direct transition from the fourth to the first orbit.

7. However, the magnitude of energy released increases with each transition.


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