Question

At what speed should the electron revolve around the nucleus of a hydrogen atom in order that it may not be pulled into the nucleus by electrostatic attraction? Take the radius of orbit of an electron as $0.5 \, Å$ , the mass of the electron as $9.1\times 10^{- 31}kg$ and charge as $1.6\times 10^{- 19 \, }C$ .

• A. $2.25\times 10^{4 }ms^{- 1}$
• B. $2.25\times 10^{5 }ms^{- 1}$
• C. $2.25\times 10^{6 }ms^{- 1}$
• D. $2.25\times 10^{7 }ms^{- 1}$

Answer 1

Answer: (C)

For motion of the electron around the nucleus,
$\frac{m v^{2}}{r}=\frac{1}{4 \pi \epsilon _{0}} \, .\frac{e \, . \, e}{r^{2}}$
$\Rightarrow \, \, v^{2}=\frac{1}{4 \pi \epsilon _{0}} \, .\frac{e^{2}}{m r}$
$\Rightarrow \quad v^2=\frac{9 \times 10^9 \times\left(1.6 \times 10^{-19}\right)^2}{9.1 \times 10^{-31} \times 0.5 \times 10^{-10}}=5 \times 10^{12}$
$\Rightarrow \, \, \, v\approx 2.25\times 10^{6} \, m \, s^{- 1}$