Question

The wavelength of first lines of Balmer series and Lyman series are related as $\frac{{\lambda }_B}{{\lambda }_L}=\frac{27}{n}$; then n is:___

Answer 1

$\frac{1}{{\lambda }_B}=R[\frac{1}{2^2}-\frac{1}{3^2}]\frac{1}{{\lambda }_L}=R[\frac{1}{1^2}-\frac{1}{2^2}]\frac{{\lambda }_B}{{\lambda }_L}=\frac{(1-\frac{1}{4})}{(\frac{1}{4}-\frac{1}{9})}=\frac{\left(\frac{3}{4}\right)}{\left(\frac{5}{36}\right)}=\frac{3\times 36}{5\times 4}=\frac{27}{5}n=5$