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  4. In the Bohr hydrogen atom, the electronic transition emitting light of longest wave length is:

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Q. In the Bohr hydrogen atom, the electronic transition emitting light of longest wave length is:

EAMCETEAMCET 1997

Solution:

In atoms, as the number of shell increases, the energy differences between the shells decreases. It means that the energy difference between $ {{n}_{1}} $ and $ {{n}_{2}} $ is higher than between $ {{n}_{2}} $ and $ {{n}_{3}} $ and in the same way energy difference is more between $ {{n}_{2}} $ and $ {{n}_{3}} $ than between $ {{n}_{3}} $ and $ {{n}_{4}}. $ We know that, $ E=hv=\frac{hc}{\lambda } $ wave length is inversely proportional to energy difference. So, in the given alternates wave length is maximum between $ {{n}_{4}} $ to $ {{n}_{3}} $ because between $ {{n}_{4}} $ and $ {{n}_{3}} $ energy difference is minimum.