Question

# If, in the first orbit of a hydrogen atom, the total energy of the electron is −21.76×10−19J, then the electric potential energy of an electron belonging to the second orbit of the same atom, will be,

A
10.88×1019 J
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B
5.44×1019 J
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C
21.76×1019 J
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D
43.52×1019 J
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Solution

## The correct option is A −10.88×10−19 JThe total energy of an electron, in hydrogen atom is, En=−me48ϵ20h2n2 ⇒En∝1n2 ⇒E1E2=n22n21 −21.76×10−19E2=41 ∴E2=−5.44×10−19 J Now, potential energy and total energy are related as, |P.E.|=2|T.E.| |P.E|=2|−5.44×10−19|=10.88×10−19 J ∴ P.E.=−10.88×10−19 J Hence, (A) is the correct answer.

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