The velocity of electron in a certain Bohr's orbit of H-atom bears the ratio `1: 275` to the velocity of light. What is the number of orbit ?

Explanation

Velocity of electron
`1/275 xx 3.0 xx 10^(10) cm s^(-1)`
`= 1.09 xx 10^8 cm s^(-1)`
Velocity of electron in nth orbit,
`v_n = (2pi Z e^2)/(nh)`
`Z = 1, e = 4.80 xx 10^(-10) esu, h = 6.63 xx 10^(-27)` erg sec
`v_n = (2 xx 3.14 xx 1 xx (4.80 xx 10^(-10))^2)/(n xx (6.3 xx 10^(-27)))`
`= (2.30 xx 10^8)/(n)`