Question

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

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

Answer 1

Answer: (D)

Electrostatic force $=$ centripetal force
$\frac{1}{4 \pi \varepsilon_{0}} \frac{Z e^{2}}{r^{2}}$
$=\frac{m v^{2}}{r}$
$\therefore v=\sqrt{\left(\frac{1}{4 \pi \varepsilon_{0}} \frac{Z e^{2}}{m r}\right)}$
$=\sqrt{\frac{9 \times 10^{9} \times 1 \times\left(1.6 \times 10^{-19}\right)^{2}}{\left(9.1 \times 10^{-31}\right) \times\left(0.1 \times 10^{-9}\right)}}$
$=1.59 \times 10^{6} ms ^{-1}$