Question

A velocity of the electron in a 3rd shell of ${Li}^{+2}is:(c\to velocityoflight)$

• A. $\frac{1}{137}c$
• B. $\frac{1}{274}c$
• C. $\frac{2}{137}c$
• D. $\frac{1}{3\times 137}c$

Answer 1

The correct option is A $\frac{1}{137}c$

The radius of the orbit is:

$r_n=\frac{n^2}{z}\times 0.529\times {10}^{-8}cm$

When n=3 and z=3

$r_3=\frac{3^2}{3}\times 0.529\times {10}^{-8}cm=1.587\times {10}^{-8}$

Now,

$v=\frac{nh}{2\pi mr}$

$=\frac{3\times 6.62\times {10}^{27}}{2\times 3.14\times 9.108\times {10}^{-28}\times 1.587\times {10}^{-8}}$

$=2.1911\times {10}^{8}cm/s$

And the velocity of the light is :

$C=3\times {10}^{10}cm/s$

So, the velocity in terms of C can be written as: $v=\frac{1}{137}c$ cm/ sec