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MHT CET 2020 (16 Oct, Shift 1) · Bohr Model: Orbits, Speed & Angular Momentum

Bohr Model: Orbits, Speed & Angular Momentum question from MHT CET 2020 (16 Oct, Shift 1)

Q96MHT CET 2020 · 16 OCT · SHIFT 1Medium

Bohr Model: Orbits, Speed & Angular Momentum

The ratio of speed of an electron in the ground state in the Bohr's first orbit of hydrogen atom to velocity of light $(c)$ is ( $h =$ Planck's constant, $\varepsilon_0 =$ permittivity of free space, $e =$ charge on electron)

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Answer: (c)

Bohr speed $v_n = \frac{Ze^2}{2\varepsilon_0 nh}$ ; for H, $n = 1$ : $v_1 = \frac{e^2}{2\varepsilon_0 h}$
$\frac{v_1}{c} = \frac{e^2}{2\varepsilon_0 hc}$
So the answer is (c) $\frac{e^2}{2\varepsilon_0 hc}$ .

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