(a)  Using Bohr's postulates, derive the expression for the orbital
    period of the electron moving in the n^{th} orbit of hydrogen atom.
(b)  Write Rydberg's formula for wavelengths of the spectral lines of
hydrogen atom spectrum, Mention to which series in the emission
spectrum of hydrogen ,H_{\alpha } line belongs.
 

 

 

 
 
 
 
 

Answers (1)
S safeer

(a) The orbital period of an electron in a Hydrogen atom is given as;
T= \frac{2\pi r_{n}}{v_{n}}-\left ( i \right )
from Bohr's postulates, we have
mv_{n}r_{n}= \frac{nh}{2\pi }
where, r_{n}= radius \: of\: n^{th}\, orbit
V_{n}= velocity \, of\, n^{th}\, orbit
m= mass.
we have,

 r_{n}= \frac{n^{2}h^{2}\varepsilon _{0}}{\pi m_{e^{2}}}
and velocity of the electron in n^{th} orbital
V_{n}= \frac{e^{2}}{2\varepsilon _{0}nh}
where,h is plank's constant
on substituting the values of r_{n} and \frac{1}{n}  in equation i we get,
T= \frac{\frac{2\pi n^{2}h^{2}\varepsilon _{0}}{\pi me^{2}}}{\frac{e^{2}}{2\varepsilon _{0}nh}}
T= \frac{4n^{2}h^{2}\varepsilon _{0}}{me^{4}}
(b) The Rydberg's formula for wavelengths of the spectral lines is given as;
\frac{1}{\lambda }= R\left ( \frac{1}{n_{1}^{2}} -\frac{1}{n_{2}^{2}}\right ) where,R is Rydberg's constant and H_{\alpha } linebelongs to Balmer Series.
 

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