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Current Loop Is a Magnet?

The ratio of ...

Question

The ratio of the energy required to remove an electron from the first three Bohr's orbits of hydrogen is:

A

3 : 2 : 1

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B

9 : 4 : 1

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C

36 : 9 : 4

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D

1 : 4 : 9

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Solution

The correct option is C 36 : 9 : 4
$E_{n} = - 13.6 \frac{z^{2}}{n^{2}} e v$
for Hydrogen $z = 1$
$E_{1} = - 13.6 e v$
$E_{2} = \frac{- 13.6}{4} e v$
$E_{3} = \frac{- 13.6}{9} e v$
ratio $= E_{1} : E_{2} : E_{3}$
$= 1 : \frac{1}{4} : \frac{1}{9}$
$= 36 : 9 : 4$

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