The ratio of speed of an electron in ground state in Bohr's first orbit of hydrogen atom

The ratio of speed of an electron in ground state in Bohr’s first orbit of hydrogen atom

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

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

e²/2ε₀hc

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

MH2002

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