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Standard IX

Chemistry

Bohr's Model of an Atom

Consider Bohr...

Question

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

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Solution

Angular momentum, radius and velocity of $H$ atom is given by ,
$l$ $α$ $n$ ,
$r$ $α$ $n^{2}$ ,
$v$ $α$ $\frac{1}{n}$
$v r l$ $α$ $n^{x}$ (given)
Substituting values of $v$ , $r$ and $l$
$v r l$ $α$ $n^{2}$
Therefore comparing with the given equation $x = 2$

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

Angular momentum, radius and velocity of H atom is given by ,l α n,r α n2,v α 1nvrl α nx (given)Substituting values of v, r and lvrl α n2 Therefore comparing with the given equation x=2

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

Angular momentum, radius and velocity of $H$ atom is given by ,
$l$ $α$ $n$ ,
$r$ $α$ $n^{2}$ ,
$v$ $α$ $\frac{1}{n}$
$v r l$ $α$ $n^{x}$ (given)
Substituting values of $v$ , $r$ and $l$
$v r l$ $α$ $n^{2}$
Therefore comparing with the given equation $x = 2$