Question

The short wavelength limit for the Lyman series of the hydrogen spectrum is $913.4A^{\circ }$. Calculate the short wavelength limit for Balmer series of the hydrogen spectrum.

Answer 1

For short wavelength of Lyman series,
$\frac{1}{{\lambda }_B}=R(\frac{1}{1^2}-\frac{1}{{\infty }^2})\frac{1}{913.4\times {10}^{-10}}=R$
For short wavelength of Balmer series,
$\frac{1}{{\lambda }_B}=R(\frac{2}{1^2}-\frac{1}{{\infty }^2})\frac{1}{{\lambda }_B}=\frac{1}{913.4\times {10}^{-10}}\times \frac{1}{4}{\lambda }_B=4\times 913.4\times {10}^{-10}\lambda =3653.6\times {10}^{-10}m=3653.6A^{\circ }$