Question

If an electron is revolving round the hydrogen nucleus at a distance of $0.1nm$, the speed should be :

• A. $2.188\times {10}^{6}m/s$
• B. $1.094\times {10}^{6}m/s$
• C. $4.376\times {10}^{6}m/s$
• D. $1.59\times {10}^{6}m/s$

Answer 1

The correct option is D $1.59\times {10}^{6}m/s$

Radius of orbit $=0.1nm$
According to formula:
$0.1\times {10}^{-9}=0.529\times {10}^{-10}\times n^2$
$\Rightarrow n^2=1.8\Rightarrow n=1.37$

So, in 2nd case:
Velocity of electron $=\frac{2.18\times {10}^6}{n}$
$\Rightarrow V=\frac{2.18}{1.37}\times {10}^6=1.59\times {10}^{6}m/s$