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Q.
What is the difference in wavelengths of the $4^{th}$ and $5^{th}$ lines of the Balmer series in the spectrum of atomic hydrogen :-
Structure of Atom
Solution:
Wavelength of $4^{\text {th }}$ line of Balmer series $\lambda_{4}$
$=\frac{1}{ R _{ H }\left(\frac{1}{4}-\frac{1}{36}\right)}=912 \times \frac{9}{2} \,\mathring{A}$
and wavelength of $5^{\text {th }}$ line of Balmer series $\lambda_{5}$
$=\frac{1}{ R _{ H }\left(\frac{1}{4}-\frac{1}{49}\right)}=\frac{912 \times 196}{45} \,\mathring{A}$
therefore $\lambda_{4}-\lambda_{5}=912\left(\frac{9}{2}-\frac{196}{45}\right)=131.7 \,\mathring{A}$