In the Bohr model of hydrogen atom, the centripetal force is furnished by the coulomb attraction between the proton and the electron. If ' r₀ ' is the radius of the ground state orbit, ' m ' is the mass, ' e ' is the charge on the electron and ' ε₀ ' is the permittivity of vacuum, the speed of the electron is (a) zero (b) (e)/(√(ε₀ r₀ m)) (c) (e)/(√(4πε₀ r₀ m)) (d) (√(4πε₀ r₀ m))/(e)

Answer: (c). Centripetal force = Coulomb force: (mv²)/(r₀) = (e²)/(4πε₀ r₀²) v² = (e²)/(4πε₀ r₀ m) So the answer is (c) v = (e)/(√(4πε₀ r₀ m)).

In the Bohr model of hydrogen atom, the centripetal force is… | MHT CET 2024 (10 May, Shift 2)

Q47MHT CET 2024 · 10 MAY · SHIFT 2Easy

Bohr Model: Orbits, Speed & Angular Momentum

In the Bohr model of hydrogen atom, the centripetal force is furnished by the coulomb attraction between the proton and the electron. If ' $r_0$ ' is the radius of the ground state orbit, ' $m$ ' is the mass, ' e ' is the charge on the electron and ' $\varepsilon_0$ ' is the permittivity of vacuum, the speed of the electron is

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Answer: (c)

Centripetal force = Coulomb force: $\frac{mv^2}{r_0} = \frac{e^2}{4\pi\varepsilon_0 r_0^2}$
$v^2 = \frac{e^2}{4\pi\varepsilon_0 r_0 m}$
So the answer is (c) $v = \frac{e}{\sqrt{4\pi\varepsilon_0 r_0 m}}$ .

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