Question

Calculate the ratio of the speed of light and the speed of electron in the first Bohr orbit of a hydrogen atom.

• A. 137
• B. 138
• C. 139
• D. 140

Answer 1

The correct option is A 137

Speed of an electron revolving in an orbit in H-like species is given by:
$=2.189\times {10}^6\frac{Z}{n}\text{m/sec}$
$\frac{Z}{n}$ for H atom = 1/1 = 1
$\therefore$ Ratio of speed of light$\left(c\right)$ to speed of an electron$\left(v\right)$ in first Bohr orbit of hydrogen atom is:
$\frac{c}{v}=\frac{3\times {10}^{8}m/s}{2.189\times {10}^{6}m/s}=137$