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The magnitude of energy, magnitude of linear momentum and magnitude of orbital radius of an electron in a hydrogen atom are E,p and r respectively, then according to Bohr’s theory of hydrogen atom, match the expressions in List-I with statements in List-II

COLUMN-I

COLUMN-II
P) Epr 1) Is independent of ‘n’
Q) $\frac{P}{E}$ 2) Is directly proportional to ‘n’
R) Er 3) Is inversely proportional to ‘n’
S) $\frac{E p}{r}$ 4) Is inversely proportional to n³
5) Is inversely proportional to n⁵

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P $\to$ 3, Q $\to$ 4, R $\to$ 1, S $\to$ 5

P $\to$ 3, Q $\to$ 2, R $\to$ 1, S $\to$ 5

P $\to$ 4, Q $\to$ 2 , R $\to$ 1, S $\to$ 5

P $\to$ 3, Q $\to$ 2, R $\to$ 4, S $\to$ 1

answer is A.

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Detailed Solution

Energy magnitude, $E α \frac{1}{n^{2}}$
Linear momentum, $p α \frac{1}{n}$
Radius of orbit, $r α n^{2}$
P) $E p r α \frac{1}{n^{2}} x \frac{1}{n} x n^{2} \to \frac{1}{n}$
Q) $\frac{p}{E} α \frac{\frac{1}{n}}{\frac{1}{n^{2}}} α n$
R) $E r α \frac{1}{n^{2}} x n^{2} \to i n d e p e n d e n t of 'n'$
S) $\frac{E p}{r} α \frac{\frac{1}{n^{2}} x \frac{1}{n}}{n^{2}} α \frac{1}{n^{5}}$

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