Bohr's Model of Hydrogen Atom

Bohr's model is too simple for atoms beyond hydrogen. In multi-electron atoms like helium, it fails because it ignores a couple of aspects. First is the electron-to-electron repulsion, and second is the shielding effect, where inner electrons reduce the nuclear pull on outer ones. Due to both, orbitals with the same principal quantum number don't have the same energy. Bohr's model of atom assumes that it should have the same energy.

According to Bohr's theory,

$K.E.=13.6\frac{z^2}{n^2}$ frequency $\left(\upsilon \right)$ of revolution of electron $\propto \frac{z^2}{n^3}$

  $v=2.18*10^6\frac{z}{n}$          

$F=\frac{k{q}_1{q}_2}{r^2}=\frac{Kz{e}^2}{r^2}\left(r\propto \frac{n^2}{z}\right)$       

$F\propto \frac{z^3}{n^4}$         

mvr = $\frac{nh}{2\pi }\left(angularmomentum\right)$  

$KE=\frac{n^2{h}^2}{8{\pi }^{2}m{r}^2}$ (Bohr's kinetic energy)

$=\frac{4h^2}{8{\pi }^{2}m{\left(4a_0\right)}^2}\left(n=2\right)$

$K.E.=\frac{1}{32{\pi }^2}\frac{h^2}{m{a}_0^2}$

Comparing with $\frac{h^2}{xm{a}_0^2}$

x = 32π² = 315.50

10x = 3155

According to Bohr's model, velocity of electron increases according to atomic number (z).

$v_e\propto \frac{z}{n}$ (z = Atomic number and n = number of shell/principal quantum number)

Similarly, velocity of electron decreases according to number of shell (i.e. principal quantum number).