Structure of Atom

According to Bohr’s postulate, the angular momentum of an electron is quantised, that is, mvr = $\frac{nh}{2\pi}$ ⇒ v = $\frac{nh}{2\pi mr}$ Now, substituting the above expression in the kinetic energy expression $\frac{1}{2} mv^2$, we get K.E. = $\frac{1}{2} m \left( \frac{nh}{2\pi mr} \right)^2$ (1) where r is the radius of Bohr’s orbit, that is, r = $a_0 \times \frac{n^2}{Z}$. For the second Bohr’s orbit of a hydrogen atom, substituting Z = 1 and n = 2, we get r = $4a_0$ where $a_0$ is a constant. Now, substituting this value of r in Eq. (1), we get K.E. = $\frac{1}{2} \times m \left( \frac{4h^2}{4\pi^2 m^2 \cdot 16 a_0^2} \right)$ = $\frac{h^2}{32\pi^2 m a_0^2}$