Answer to Question #271193 in Physics for Almas

Question

Find the frequency of revolution of the electron in the classical model of the hydrogen atom. In what region of the spectrum are electromagnetic waves of this frequency?

Answer 1

$\nu=\frac{v_n}{2\pi r_n}$

$mv_nr_n=\frac{nh}{2\pi}\to v_n=\frac{nh}{2\pi mr_n}$

$m\frac{v_n^2}{r_n}=\frac{q^2}{4\pi\epsilon_0r_n^2}\to r_n=\frac{h^2\epsilon_0}{\pi m q^2}\cdot n^2$

$v_n=\frac{nh}{2\pi mr_n}=\frac{nh}{2\pi m}\frac{\pi m q^2}{h^2\epsilon_0n^2}=\frac{q^2}{2nh\epsilon_0}$

$\nu_n=\frac{v_n}{2\pi r_n}=\frac{q^2}{2\pi \cdot2nh\epsilon_0}\cdot \frac{\pi m q^2}{h^2\epsilon_0n^2}=$

$=\frac{q^4 m}{4h^3\epsilon_0^2}\cdot\frac{1}{n^3}$

For $n=1$ $\nu_1=\frac{(1.6\cdot10^{-19})^4\cdot9.1\cdot10^{-31}}{4\cdot (6.62\cdot10^{-34})^3\cdot(8.85\cdot10^{-12})^2}\cdot\frac{1}{1^3}\approx6.56\cdot10^{15}\ (Hz)$

which corresponds to ultraviolet region.