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JEE Advanced levelSingle correct optionDifficulty 3 of 3as096

The $n = 2$ level of a hydrogen-like ion has energy $- 30.6 eV$ (take $E_{1} = - 13.6 eV$ for hydrogen and $a_{0} = 0.529 \overset{˚}{A}$ ). The radius of its third Bohr orbit is

A $4.76 \overset{˚}{A}$
B $2.38 \overset{˚}{A}$
C $1.59 \overset{˚}{A}$
D $0.53 \overset{˚}{A}$

Answer: C

- 30.6 = - 13.6 Z^{2} /4

gives

Z^{2} = 9

,

Z = 3

. Then

r_{3} = a_{0} n^{2} / Z = 0.529 \times 9/3 = 1.59 \overset{˚}{A}

.

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