Question

If the Bohr model of hydrogen atom, the electron is treated as a particle going in a circle with the centre at the proton. The proton itself is assumed to be fixed in an inertial frame. The centripetal force is provided by the Coloumb attraction. In the ground state, the electron goes round the proton in a circle of radius $5.3\times {10}^{-11}m$ . Find the speed of the electron in the ground state. Mass of the electron $=9.1\times {10}^{-31}kg$ and charge of the electron $=1.6\times {10}^{-19}C$

Answer 1

Electron revolves around the proton in a circle having proton at the center.

Centripetal force is provided by coulomb attraction

$r=5.3\times {10}^{-11}m$

$m=$ mass of electron $=9.1\times {10}^{-3}kg$

charge of electron $=1.6\times {10}^{-19}C$

For the particular charge particle, the centripetal force is balanced by the electrostatic force.

Centripetal force = Electrostatic force

$\frac{m{v}^2}{r}=k\frac{q^2}{r^2}$

$\Rightarrow v^2=\frac{k{q}^2}{rm}=\frac{9\times {10}^9\times 1.6\times 1.6\times {10}^{-38}}{5.3\times {10}^{-11}\times 9.1\times {10}^{-31}}$

$=\frac{23.04}{48.23}\times {10}^{13}$

$\Rightarrow v^2=4.077\times {10}^{13}=4.7\times {10}^{12}$

$\Rightarrow v=\sqrt{4.7\times {10}^{12}}=2.2\times {10}^{6}m/sec$