Physics Atoms

This theory simply stated that there exist stationary orbits around the nucleus in which electrons rotate without dissipating any type of energy. And if the electrons try to change their orbits, then there will be a gain or loss of energy depending on the situation.

The spectrum of H-atom is formulated and drawn by Bohr's model. These spectrums are line spectrum. Lyman series lies in UV region, Balmer Partly lies UV and partly in the visible region and Paschen series lies in the infrared region.

The spectrum of H-atom is formulated and drawn by Bohr's model. These spectrums are line spectrum. Lyman series lies in UV region, Balmer Partly lies UV and partly in the visible region and Paschen series lies in the infrared region.

  $\Delta E=13.6\left(\frac{1}{1^2}-\frac{1}{5^2}\right)=13.6*\frac{24}{25}eV$

$\Rightarrow \frac{hc}{\lambda }=13.6*\frac{24}{25}eV..........\left(1\right)$          

With the help of conservation of linear momentum, we can write

$\frac{h}{\lambda }=m_H{v}_H\Rightarrow \frac{hc}{\lambda }=c{m}_H{v}_H\Rightarrow v_H=\frac{\frac{hc}{\lambda }}{c{m}_H}=\frac{13.6*\frac{24}{25}*1.6*10^{-19}}{3*10^8*1.67*10^{-27}}=4.17m/s$           

$h{f}_1=R\left(\frac{1}{1^2}-\frac{1}{3^2}\right)=R*\frac{8}{9}$

$h{f}_2=R\left(\frac{1}{1^2}-\frac{1}{2^2}\right)=R*\frac{3}{4}$

$\frac{f_1}{f_2}=\frac{8/9}{3/4}=\frac{32}{27}$

f2 = f1 * $\left(\frac{27}{32}\right)$

$=\left(2.92*10^{15}\right)*\left(\frac{27}{32}\right)$

$=2.46*10^{15}Hz$

$\mathrm{\Delta }{E}_1=\frac{12400\mathrm{e}\mathrm{V}\text{?}}{1085\text{?}}=11.43\mathrm{e}\mathrm{V}$

$\mathrm{\Delta }{E}_2=\frac{12400}{304}\mathrm{e}\mathrm{V}=40.80\mathrm{e}\mathrm{V}$

$\mathrm{\Delta }{E}_1+\mathrm{\Delta }{E}_2=54.4\mathrm{e}\mathrm{V}\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)\Rightarrow 52.23=54.4\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)$

If $n_1=1\mathrm{}{n}_2=5$

$E=\frac{\text{Energy}}{\text{time}*\text{Area}}\Rightarrow \left[E\right]=\frac{\left[\text{Energy}\right]}{\left[\text{time}\right]\left[\text{Area}\right]}=\frac{M{L}^2{T}^{-2}}{L^{2}T}$

$\left[E\right]=M{L}^0{T}^{-3}$

(hc/λ) = 13.6Z² (1/1² - 1/4²) = 13.6Z² (3/4) ; [λ = (4/3)k]

β line of Paschen
(hc/λ') = 13.6Z² (1/9 - 1/25)
λ = k * (9*25/16) ; λ' = (3/4)λ * (9*25/16) = (3³*5²/2? )λ

$v\propto \frac{z}{n}$  

              $v=k\frac{z}{n}$   [K ® constant]

              for 3^rd orbit of He⁺

              $v_{H{e}^{+}}=\frac{k*2}{3}=\frac{2k}{3}$               - (1)

              $v_H=\frac{k*1}{3}=\frac{k}{3}$                    - (2)

              $\frac{v_{H{e}^{+}}}{v_H}=2:1$