Q83 / 90 · JEE Main 2017 (09 Apr Online) · Physics

The acceleration of an electron in the first orbit of the hydrogen atom ( $n = 1$ ) is :

A
$\frac{h^{2}}{4 π m^{2} r^{3}}$
B
$\frac{h^{2}}{π^{2} m^{2} r^{3}}$
C
$\frac{h^{2}}{8 π^{2} m^{2} r^{3}}$
Correct answer
D
$\frac{h^{2}}{4 π^{2} m^{2} r^{3}}$

Solution

For

H -

atom

(n = 1)

\frac{m v^{2}}{r} = \frac{1}{4 π ϵ_{o}} \frac{e^{2}}{r^{2}} . . . (1)

m v r = \frac{h}{2 π} . . . (2)

On squaring

(2)

m^{2} v^{2} r^{2} = \frac{h^{2}}{4 π^{2}}

On dividing both sides by

r^{3},

\frac{m^{2} v^{2}}{r} = \frac{h^{2}}{4 π r^{3}} \Rightarrow \frac{v^{2}}{r} = \frac{h^{2}}{4 π^{2} r^{3} m^{2}}

Acceleration

= \frac{h^{2}}{4 π^{2} r^{3} m^{2}}

.

Hence, the correct answer is option: 'D'.

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