Question

A hydrogen atom consist of a proton and an electron that revolves round it in a circular orbit with radius $5.30\times {10}^{-5}cm$. If the electron moves s that its centrifugal force is just equal to the electrostatic force then the speed is:

• A. $4.40\times {10}^{12}m/s$
• B. $4.40\times {10}^{6}m/s$
• C. $2.20\times {10}^{6}m/s$
• D. $1.10\times {10}^{6}m/s$

Answer 1

The correct option is C $2.20\times {10}^{6}m/s$

Centrifugal force$=$ electrostatic force

$\Rightarrow \frac{m{v}^2}{R}=\frac{k{e}^2}{R^2}\Rightarrow v^2=\frac{k{e}^2}{mR}\Rightarrow v=\sqrt{\frac{k}{mR}}e\Rightarrow v=\sqrt{\frac{9\times {10}^9}{9.1\times {10}^{-31}\times 5.3\times {10}^{-5}\times {10}^{-2}}}\times 1.6\times {10}^{-19}=2.2\times {10}^{6}m/s$