Question

If an electron is revolving around the hydrogen nucleus at a distance of $0.1nm$ , what should be its speed ?

• A. $2.188\times 10^{6}m{s}^{-1}$
• B. $1.094\times 10^{6}m{s}^{-1}$
• C. $4.376\times 10^{6}m{s}^{-1}$
• D. $1.59\times 10^{6}m{s}^{-1}$

Answer 1

Answer: (D)

Electrostatic force $=$ centripetal force
$\frac{1}{4\pi {\epsilon }_0}\frac{Z{e}^2}{r^2}$
$=\frac{m{v}^2}{r}$
$\therefore v=\sqrt{\left(\frac{1}{4\pi {\epsilon }_0}\frac{Z{e}^2}{mr}\right)}$
$=\sqrt{\frac{9\times 10^9\times 1\times {\left(1.6\times 10^{-19}\right)}^2}{\left(9.1\times 10^{-31}\right)\times \left(0.1\times 10^{-9}\right)}}$
$=1.59\times 10^{6}m{s}^{-1}$