Answer to Question #157816 in Classical Mechanics for Sharmila devi

Question

A charged particle in moving under the influence of a point nucleus. Find the orbit of the particle and periodic time in the case of an elliptical orbit.

Answer 1

Answer

A charged particle(let electron) in moving under the influence of a point nucleus.

Then central force is given

$F=\frac{-ze^2}{r^2}$ $;k=ze^2$

E=$\frac{-k}{2a}=\frac{-ze^2}{2a}$

Eccentricity

$\epsilon=\sqrt{1+\frac{2Eh^2}{mz^2e^4}}=\sqrt{1+\frac{h^2}{amz^2e^2}}$

This shows elliptical path.

Now time period

$T=\frac{4\pi ^2a^2m}{k}=\frac{2m}{e}\sqrt{\frac{ma^2}{z}}$