Question

A sample of hydrogen atoms in the ground state is excited by a monochromatic radiation of wavelength $\lambda \stackrel{o}{\text{A}}$. The resulting spectrum consists of a maximum of 15 different lines. What is the wavelength $\lambda$?
($R_H=109737{\text{cm}}^{-1}$)

• A. $937.3\stackrel{o}{\text{A}}$
• B. $1025\stackrel{o}{\text{A}}$
• C. $1236\stackrel{o}{\text{A}}$
• D. None of these

Answer 1

The correct option is A $937.3\stackrel{o}{\text{A}}$

For a transition from $n_2$ to $n_1$, the maximum possible lines is given by $\frac{(n_2-n_1)(n_2-n_1+1)}{2}$
For the given H-atom ($n_1=1$), 15 lines are observed.
$15=\frac{(n_2-1)n_2}{2}$
$\Rightarrow n_2=6$
Thus, the electron is excited upto the 6th energy level.
So,
$\frac{1}{\lambda }=R_H[\frac{1}{1^2}-\frac{1}{6^2}]$

$=109677\times \frac{35}{36}{\text{cm}}^{-1}$

$\lambda =9.373\times {10}^{-6}{\text{cm}}^{-1}=937.3\stackrel{o}{\text{A}}$