Question

The speed of the electron in the $1$st orbit of the hydrogen atom in the ground state is: ($c$ is the velocity of light)

• A. $\frac{c}{1.37}$
• B. $\frac{c}{1370}$
• C. $\frac{c}{13.7}$
• D. $\frac{c}{137}$

Answer 1

The correct option is D $\frac{c}{137}$

Velocity of electron in Bohr orbit = $V_0\frac{z}{n}$

where $V_0=2.18\times {10}^{6}m/s$

For hydrogen (z=1),

$V_1=V_0=2.18\times {10}^{6}m/s$

Speed of light = 3.0 \times 10^8 m/s$

Let $\frac{c}{x}=V_1$

$⟹cfrac3\times {10}^{8}x=2.18\times {10}^6$

$x=137$

Therefore $\frac{c}{137}$ (Ans)