Question

What is the difference in wavelengths of the $4^{th}$ and $5^{th}$ lines of the Balmer series in the spectrum of atomic hydrogen :-

• A. $131\mathring{A}$
• B. $520\mathring{A}$
• C. $390\mathring{A}$
• D. $262\mathring{A}$

Answer 1

Answer: (A)

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 ${\lambda }_4-{\lambda }_5=912\left(\frac{9}{2}-\frac{196}{45}\right)=131.7\mathring{A}$