In hydrogen atom, electron excites from ground state to higher energy state and its orbital velocity is reduced to ((1/3))rd of its initial value. The radius of the orbit in the ground state is R. The radius of the orbit in that higher energy state is

Question

In hydrogen atom, electron excites from ground state to higher energy state and its orbital velocity is reduced to ((1/3))rd of its initial value. The radius of the orbit in the ground state is R. The radius of the orbit in that higher energy state is (A) 9 R (B) 2 R (C) 3 R (D) 27 R

Tardigrade Admin · Accepted Answer

Velocity of electron in n text th orbit is inversely proportional to n. v n propto ( 1 / n ) Given: ( v n / v 1 )=( 1 / 3 ) Longrightarrow n = 3 Radius of electron in n text th orbit is proportional to n 2. r n propto n 2 Hence, r 3=9 r 1= 9 R

Q. In hydrogen atom, electron excites from ground state to higher energy state and its orbital velocity is reduced to $(\frac{1}{3}) r d$ of its initial value. The radius of the orbit in the ground state is $R$ . The radius of the orbit in that higher energy state is

9 R

2 R

3 R

27 R

Velocity of electron in $n^{th}$ orbit is inversely proportional to $n$ .
$v_{n} \propto \frac{1}{n}$
Given:
$\frac{v _{n}}{v _{1}} = \frac{1}{3}$
$⟹ n = 3$
Radius of electron in
$n^{th}$
orbit is proportional to
$n^{2}$ .
$r_{n} \propto n^{2}$
Hence, $r_{3} = 9 r_{1} = 9 R$

Q. In hydrogen atom, electron excites from ground state to higher energy state and its orbital velocity is reduced to (31​)rd of its initial value. The radius of the orbit in the ground state is R. The radius of the orbit in that higher energy state is

9 R

2 R

3 R

27 R

Velocity of electron in nth orbit is inversely proportional to n. vn​∝n1​ Given: v1​vn​​=31​ ⟹n=3 Radius of electron in nth orbit is proportional to n2. rn​∝n2 Hence, r3​=9r1​=9R

Q. In hydrogen atom, electron excites from ground state to higher energy state and its orbital velocity is reduced to $(\frac{1}{3}) r d$ of its initial value. The radius of the orbit in the ground state is $R$ . The radius of the orbit in that higher energy state is

Velocity of electron in $n^{th}$ orbit is inversely proportional to $n$ .
$v_{n} \propto \frac{1}{n}$
Given:
$\frac{v _{n}}{v _{1}} = \frac{1}{3}$
$⟹ n = 3$
Radius of electron in
$n^{th}$
orbit is proportional to
$n^{2}$ .
$r_{n} \propto n^{2}$
Hence, $r_{3} = 9 r_{1} = 9 R$