Assuming the atom is in the ground state, the expression for the magnetic field at a point nucleus in hydrogen atom due to circular motion of electron is [ μ₀ = permeability of free space, m = mass of electron, ε₀ = permittivity of free space, h = Planck's constant ] (a) (μ₀ e⁷ π m²)/(8ε₀³ h⁵) (b) (μ₀ e⁵ π m³)/(8ε₀³ h⁵) (c) (μ₀ e⁵ π² m²)/(8ε₀² h⁴) (d) (μ₀ e⁷ π² m²)/(8ε₀³ h⁵)

Answer: (a). Bohr ground state: r = (ε₀ h²)/(π m e²), v = (e²)/(2ε₀ h). Current I = (ev)/(2π r), so B = (μ₀ I)/(2r) = (μ₀ e v)/(4π r²). B = (μ₀ e)/(4π)·(e²)/(2ε₀ h)·(π² m² e⁴)/(ε₀² h⁴) = (μ₀ e⁷ π m²)/(8ε₀³ h⁵) So the answer is (a).

Assuming the atom is in the ground state, the expression for the… | MHT CET 2021 (22 Sep, Shift 1)

Q81MHT CET 2021 · 22 SEP · SHIFT 1Difficult

Biot-Savart Law & Circular Coils

Assuming the atom is in the ground state, the expression for the magnetic field at a point nucleus in hydrogen atom due to circular motion of electron is [ $\mu_0 =$ permeability of free space, $m =$ mass of electron, $\epsilon_0 =$ permittivity of free space, $h =$ Planck's constant ]

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Answer: (a)

Bohr ground state: $r = \dfrac{\epsilon_0 h^2}{\pi m e^2}$ , $v = \dfrac{e^2}{2\epsilon_0 h}$ .
Current $I = \dfrac{ev}{2\pi r}$ , so $B = \dfrac{\mu_0 I}{2r} = \dfrac{\mu_0 e v}{4\pi r^2}$ .
$B = \dfrac{\mu_0 e}{4\pi}\cdot\dfrac{e^2}{2\epsilon_0 h}\cdot\dfrac{\pi^2 m^2 e^4}{\epsilon_0^2 h^4} = \dfrac{\mu_0 e^7 \pi m^2}{8\epsilon_0^3 h^5}$
So the answer is (a).

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