Solved: PHYSICS Question for NEET

NEET PHYSICSMedium

In the Bohr's model of a hydrogen atom, the centripetal force is furnished by the Coulomb attraction between the proton and the electron. If a₀ is the radius of the ground state orbit, m is the mass and e is the charge on the electron, ε₀ is the vacuum permittivity, the speed of the electron is:

zero

e / √(ε₀a₀m)

e / √(4\pi ε₀a₀m)

√(4\pi ε₀a₀m) / e

Step-by-Step Solution

In Bohr's model, the necessary centripetal force ( $F_c$ ) for the electron's circular motion is provided by the electrostatic Coulomb attraction ( $F_e$ ) between the nucleus and the electron.

Formula for centripetal force: $F_c = \frac{mv^2}{r}$
Formula for Coulomb force: $F_e = \frac{1}{4\pi\epsilon_0} \frac{e^2}{r^2}$ (for Hydrogen, Z=1)
Equating the forces: $\frac{mv^2}{r} = \frac{1}{4\pi\epsilon_0} \frac{e^2}{r^2}$
Solving for velocity ( $v$ ): $mv^2 = \frac{e^2}{4\pi\epsilon_0 r} \Rightarrow v^2 = \frac{e^2}{4\pi\epsilon_0 mr}$ $v = \frac{e}{\sqrt{4\pi\epsilon_0 mr}}$

Given that the radius of the ground state orbit is $a_0$ , we substitute $r = a_0$ to get: $v = \frac{e}{\sqrt{4\pi\epsilon_0 a_0 m}}$ .

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