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Consider Bohr's theory for hydrogen atom. The magnitude of orbit angular momentum, orbit radius and velocity of the electron in nth energy state in a hydrogen atom are l, rand v respectively. Find out the value of 'x', if product of v, r and l (vrl) is directly proportional to $n^{x}$ .

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answer is 2.

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Detailed Solution

It is known that;

$v \propto \frac{1}{n}; r \propto n^{2}; l \propto n \Rightarrow v r l \propto n^{2} \Rightarrow x = 2$

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Consider Bohr's theory for hydrogen atom. The magnitude of orbit angular momentum, orbit radius and velocity of the electron in nth energy state in a hydrogen atom are l, rand v respectively. Find out the value of 'x', if product of v, r and l (vrl) is directly proportional to nx.