Physics Atoms

Based on what classical electromagnetic theory says, we know that an accelerated charged particle must radiate energy or electromagnetic waves. That remains continuous. 

By looking at the Rutherford's atomic model we can assume that electrons would revolve around the nucleus, which in this logic, held in orbit by electrostatic attraction. The reason is that, their path is circular that's always accelerating. That would mean the electron would start to lose energy and finally let the atom to implode. But that doesn't happen. Atoms are stable and that's where classical physics that led to Rutherford model failed. 

1/λmin = R [1/1² - 1/∞²] = R [n=∞ → n=1]
1/λmax = R [1/1² - 1/2²] = 3R/4 [n=2 → n=1]
⇒ Δλ ⇒ 4/3R - 1/R ⇒ 1/3R ⇒ 340
For Paschan ⇒ 1/λmin = R [1/9] [n=∞ → h=3]
⇒ 1/λmax = R [1/9 - 1/16] = 7R/144
⇒ Δλ = 81/7R

Density $=\frac{M}{V}=\frac{1.67*{10}^{-27}*A}{\frac{4}{3}\pi (1.3{)}^3*{10}^{-45}*A}\approx {10}^{17}$

$=5\mathrm{M}\left({\mathrm{u}}^2-\frac{119{\mathrm{G}\mathrm{M}}_{\mathrm{e}}}{200\mathrm{R}}\right)$

$T=\frac{2\pi }{\omega }=2\pi \frac{r}{v}\propto \frac{n^2}{\frac{1}{n}}\propto n^3$

$\therefore \mathrm{}v=\frac{1}{\mathrm{T}}\propto \frac{1}{{\mathrm{n}}^3}$

$\frac{v_2}{v_1}=\frac{1^3}{2^3}=\frac{1}{8}$

$\mathrm{}N\propto \frac{1}{{\mathrm{s}\mathrm{i}\mathrm{n}}^4?\left(\frac{\theta }{2}\right)}$

Kindly consider the following Image