The radius of which of the following orbit is same

The radius of which of the following orbit is same as that of the first Bohr’s orbit of a hydrogen atom?

A) Li 2+ (n=2)

B) Li 2+ (n=3)

C) Be 3+ (n=2)

D) He + (n=2)

Answer:

C) Be 3+ (n=2)

Explanation:

$I_{H} = 0.529 A \circ \to I_{n} = I_{H} \times Z n ^{2}$

For $L i^{2+} (n = 2)$ ,

$I_{L i 2+} = I_{H} \times 3 ( 2 ) ^{2} = 9 I ^{H} \times 4$

For $L i^{2+} (n = 3)$ ,

$I_{L i 2+} = I_{H} \times 3 ( 3 ) ^{3} = 3 r_{H}$

For

B e^{3+} (n = 2)

I_{B e 3+} = I_{H} \times 4 ( 2 ) ^{2} = I_{H}

For

H e^{+} (n = 2)

I_{H e +} = I_{H} \times 2 ( 2 ) ^{2} = 2 r_{H}

This has the same radius as that of the first Bohr’s orbit of the atom.