What is the moment of inertia of the electron moving in second Bohr orbit of hydrogen atom? [ h = Planck's constant, m = mass of electron, ε₀ = permittivity of free space, e = charge on electron] (a) 4ε₀²h⁴π²me⁴ (b) 8mε₀²h⁴π²e⁴ (c) 16ε₀²h⁴π²me⁴ (d) ε₀²h⁴16π²me⁴

Answer: (c). Bohr radius: rn = (n²ε₀ h²)/(π m e²), so r₂ = (4ε₀ h²)/(π m e²). I = mr₂² = m·(16ε₀² h⁴)/(π² m² e⁴) I = (16ε₀² h⁴)/(π² m e⁴), so the answer is (c).

What is the moment of inertia of the electron moving in second Bohr… | MHT CET 2023 (10 May, Shift 2)

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Angular Momentum & its Conservation

What is the moment of inertia of the electron moving in second Bohr orbit of hydrogen atom? [ $\mathrm{h} =$ Planck's constant, $\mathrm{m} =$ mass of electron, $\varepsilon_0 =$ permittivity of free space, $\mathrm{e} =$ charge on electron]

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Answer: (c)

Bohr radius: $r_n = \dfrac{n^2\varepsilon_0 h^2}{\pi m e^2}$ , so $r_2 = \dfrac{4\varepsilon_0 h^2}{\pi m e^2}$ .
$I = mr_2^2 = m\cdot\dfrac{16\varepsilon_0^2 h^4}{\pi^2 m^2 e^4}$
$I = \dfrac{16\varepsilon_0^2 h^4}{\pi^2 m e^4}$ , so the answer is (c).

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