Question

Calculate the wavelength of the first number of Balmer series of hydrogen spectrum (R for hydrogen = 1.09678 $\times$ 10${}^7$ m${}^{-1}$).

• A. 2188$\times$ 10${}^{-10}$ m
• B. 656 $\times$ 10${}^{-10}$ m
• C. 6564 $\times$ 10${}^{-10}$ m
• D. None of these

Answer 1

Answer: (C)

6564 $\times$ 10${}^{-10}$ m

Balmer series: $\frac{1}{\lambda }=R[\frac{1}{2^2}-\frac{1}{n^2}]$, $n=3,4,5,$...

When $n=3$(first member of Balmer series),

$\frac{1}{\lambda }=1.09678\times {10}^7$ ($\frac{1}{2^2}$ - $\frac{1}{3^2}$)

$=1.09678\times {10}^7\times \frac{5}{36}$

$\therefore \lambda =6564\times {10}^{-10}m$