Frequency of the series limit of Balmer series of hydrogen atom in terms of Rydberg's constant (R) and…
Frequency of the series limit of Balmer series of hydrogen atom in terms of Rydberg's constant (R) and velocity of light (c) is
$4 \mathrm{Rc}$
$\frac{4}{\mathrm{Rc}}$
$\mathrm{Rc}$
$\frac{\mathrm{Rc}}{4}$
Solution
Wavelength of Balmer series is given as, $\frac{1}{\lambda}=\mathrm{R}\left(\frac{1}{\mathrm{n}_1^2}-\frac{1}{\mathrm{n}_2^2}\right)$ where $\mathrm{n}_1=2$
For series limit, $\mathrm{n}_2=\infty$
$\therefore \quad \frac{1}{\lambda}=\mathrm{R}\left(\frac{1}{4}-\frac{1}{\infty}\right)=\mathrm{R}\left(\frac{1}{4}\right)$
Now, $v=\frac{c}{\lambda}$
$\therefore \quad v=\frac{R c}{4}$