Question

Calculate the ratio of the velocity of light to the velocity of electron in the first orbit of a hydrogen atom. $(h=6.624\times {10}^{-27}erg-sec;m_e=9.108\times {10}^{-28}g;r_{n=1}=0.529\times {10}^{-8}cm)$

• A. 1
• B. 137
• C. 6
• D. 225

Answer 1

The correct option is B 137

According to Bohr's postulate, velocity of an electron in Bohr orbit can be given by:
$v_n=2.189\times {10}^6\frac{Z}{n}m/s$
Since for H, Z = 1. putting up the values
$v_n=2.189\times {10}^{6}m/s$
The ratio of the velocity of light (c) to the velocity of electron in the first orbit of a hydrogen atom (v)
$\frac{c}{v}=\frac{3\times {10}^8}{2.189\times {10}^6}=137$