10.1 Radius of Orbit

3.1 Properties of matter waves
3.2 Application of de Broglie Hypothesis

5.1 Laws of Photoelectric emission
5.2 Photoelectric equation
5.3 Photoelectric Current
5.4 Stopping potential
5.5 Graph between $K{E_{max}}$ and frequency

8.1 Surface exposed to normal radiation
8.2 Surface exposed to radiation inclined at an angle

10.1 Radius of Orbit
10.2 Velocity of electron in the $n^th$ orbit
10.3 Orbital frequency of electron

11.1 Hypothetical Atomic Energy Level

13.1 Recoil speed of electron on emission of a photon

As centripetal force = Force of attraction

$$\begin{equation} \begin{aligned} \frac{{m{v^2}}}{r} = \frac{1}{{4\pi {\varepsilon _0}}}\frac{{(Ze)(e)}}{{{r^2}}}...(i) \\ mvr = \frac{{nh}}{{2\pi }}...(ii) \\\end{aligned} \end{equation} $$

From equation $(ii)$, $$ v = \frac{{nh}}{{2\pi mr}} $$

Substituting the value of $v$ in Eq. $(i)$, we get

$$\begin{equation} \begin{aligned} {r_n} = \frac{{{n^2}{h^2}{\varepsilon _0}}}{{\pi m{e^2}Z}} \\ \Rightarrow {r_n} = (0.53)\frac{{{n^2}}}{Z}\mathop {\text{A}}\limits^0 \\\end{aligned} \end{equation} $$

Clearly, for $H$-like atoms (one electron species) ${r_n} \propto \frac{{{n^2}}}{Z}$.

This also implies that the stationary orbits are not equally spaced.