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Q.

The radius of $n^{t h}$ orbit $r_{n}$ in terms of Bohr radius $(a_{0})$ for a hydrogen atom is given by the relation:

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a

$n^{3} a_{0}$

b

$n a_{0}$

c

$\sqrt{n} a_{0}$

d

$n^{2} a_{0}$

answer is C.

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Detailed Solution

The radius of $n^{t h}$ orbit, $r_{n} = n^{2} \frac{h^{2} ε_{0}}{π m e^{2}}$

where $\frac{h^{2} ε_{0}}{π m e^{2}} = a_{0}$ (Bohr radius)

Hence, $r_{n} = n^{2} a_{0}$

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The radius of nth orbit rn in terms of Bohr radius a0 for a hydrogen atom is given by the relation: