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Standard XII

Chemistry

Bohrs Derivations

Consider Bohr...

Question

Consider Bohr's theory for hydrogen atom. The magnitude of angular momentum, orbit radius and frequency of the electron in $n^{t} h$ energy state in a hydrogen atom are, $r$ and $f$ respectively. find out the value of $X$ , if ( $f r l$ ) is directly proportional to $n^{x}$ .

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Solution

The correct option is B 0
We know that-

$r \propto n^{2}$

$v \propto \frac{1}{n}$

and $l = \frac{n h}{2 π} ⟹ l \propto n$

$f = \frac{1}{T} = \frac{v}{2 π r}$

$⟹ f \propto \frac{1}{n^{3}}$

Hence, $f r l \propto n^{0}$

Hence, $x = 0$

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Consider Bohr's theory for hydrogen atom. The magnitude of angular momentum, orbit radius and frequency of the electron in nth energy state in a hydrogen atom are, r and f respectively. find out the value of X, if (frl) is directly proportional to nx.

The correct option is B 0We know that-r∝n2v∝1nand l=nh2π⟹l∝nf=1T=v2πr⟹f∝1n3Hence, frl∝n0 Hence, x=0

Consider Bohr's theory for hydrogen atom. The magnitude of angular momentum, orbit radius and frequency of the electron in $n^{t} h$ energy state in a hydrogen atom are, $r$ and $f$ respectively. find out the value of $X$ , if ( $f r l$ ) is directly proportional to $n^{x}$ .

The correct option is B 0
We know that-

$r \propto n^{2}$

$v \propto \frac{1}{n}$

and $l = \frac{n h}{2 π} ⟹ l \propto n$

$f = \frac{1}{T} = \frac{v}{2 π r}$

$⟹ f \propto \frac{1}{n^{3}}$

Hence, $f r l \propto n^{0}$

Hence, $x = 0$