The ratio of speed of an electron in ground state in Bohr’s first orbit of hydrogen atom to velocity of light in air (c ) is

Options

(a) e²/2ε₀hc
(b) 2e²ε₀/hc
(c) e³/2ε₀hc
(d) 2ε₀hc/e²

Correct Answer:

e²/2ε₀hc

Explanation:

Velocity of electron in nᵗʰ orbit = αcz / n
where α = (e²/4πε₀) [1 / c(h/π)] = e²/2ε₀hc
v / c = αz / n = (e² × 1) / 2ε₀hc × 1 = e²/2ε₀hc