Which one of the relations is correct between time period and number of orbits while an electron is revolving in an orbit?

Question

Which one of the relations is correct between time period and number of orbits while an electron is revolving in an orbit? (A)  n2  (B)  (1/n2)  (C)  n3  (D)  (1/n)

Tardigrade Admin · Accepted Answer

Time required for electron to go around once is

T = \frac{2 π r _{n}}{v _{n}} ?

(i)
where

r_{n}

is radius of

n^{t h}

orbit and

v_{n}

is velocity.
Multiply and divide Eq. (i) by

m v_{n}^{2}

, we get

T = \frac{2 πm r _{n} v _{n}}{m v _{n}^{2}} = π \frac{nh}{\frac{1}{2} m v _{n}^{2}} = π \frac{nh}{K _{n}}

where

K_{n}

is kinetic energy in

n^{t h}

orbit,

T = - π \frac{nh}{E}

T = \frac{h}{2} n \frac{n ^{2}}{13.6 e V} (∵ h = \frac{h}{2 π}

and

E = - \frac{13.6}{n ^{2}})

\Rightarrow T \propto n^{3} .

Q. Which one of the relations is correct between time period and number of orbits while an electron is revolving in an orbit?

$n^{2}$

$\frac{1}{n ^{2}}$

$n^{3}$

$\frac{1}{n}$

Q. Which one of the relations is correct between time period and number of orbits while an electron is revolving in an orbit?

n2

n21​

n3

n1​

$n^{2}$

$\frac{1}{n ^{2}}$

$n^{3}$

$\frac{1}{n}$