Question

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

• A. $937.3\mathring{A}$
• B. $1025\mathring{A}$
• C. $1236\mathring{A}$
• D. $2000\mathring{A}$

Answer 1

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

Since the number of different lines is 15, the excited state must be n = 6. As only then the number of lines in Lyman = 5, Balmer = 4, Paschen = 3, Brackett = 2, Pfund = 1. Sum of those different lines = 5 + 4 + 3 + 2 + 1 = 15.

$v^{-}=1/\lambda =R_H[1/n_1^2-1/n_2^2]$

$1/\lambda =10973700[1/1^2-1/6^2]m^{-1}$

$1/\lambda =10973700\left[35/36\right]$

$\lambda =937.3\mathring{A}$