Question

A hydrogen atom in the ground state is excited by monochromatic radiation of wavelength $\lambda \mathring{A}$. The resulting spectrum consists of maximum $15$ different lines. What is the wavelength $\lambda$? $(R_H=109737c{m}^{-1})$

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

Answer 1

The correct option is A $937.3\mathring{A}$

Resulting spectrum consists of maximum 15 different lines,

So, total lines in spectrum $=\frac{n_2(n_2-n_1)}{2}=15$

As the $n_1$ is given $1$ so the $n_2$ will be $6$.

To calculate $\lambda$, apply this formula-

$\frac{1}{\lambda }=R{Z}^2\times \frac{1}{n_2^2}-\frac{1}{n_1^2}$

$\frac{1}{\lambda }=R{Z}^2\times \frac{1}{6^2}-\frac{1}{1^2}$

$\lambda =\frac{36}{35}\times \frac{1}{R}$, $(Z=1)$

$\lambda =\frac{36}{35}\times 912(A{)}^o$, [$\frac{1}{R}=912$]

$\lambda =937.3A^o$