The wavelength of the first spectral line in the Balmer series of hydrogen atom is $6561\, \mathring{A}$. The wavelength of the second spectral line in the Balmer series of singly ionized helium atom is
- $1215\mathring{A}$
- $16405\mathring{A}$
- $2430\mathring{A}$
- $4687\mathring{A}$
The Correct Option is A
Solution and Explanation
$\frac{1}{\lambda}=RZ^2\bigg(\frac{1}{n^2_f}-\frac{1}{n^2_i}\bigg)$
In the transition from $n_i\rightarrow n_f$
$\therefore\lambda?\frac{1}{Z^2\bigg(\frac{1}{n^2_f}-\frac{1}{n^2_i}\bigg)}$
$\therefore\frac{\lambda_2}{\lambda_1}=\frac{Z^2_1\bigg(\frac{1}{n^2_f}-\frac{1}{n^2_i}\bigg)_1}{Z^2_2\bigg(\frac{1}{n^2_f}-\frac{1}{n^2_i}\bigg)_2},$
${\lambda_1}=\frac{\lambda_1Z^2_1\bigg(\frac{1}{n^2_f}-\frac{1}{n^2_i}\bigg)_1}{Z^2_2\bigg(\frac{1}{n^2_f}-\frac{1}{n^2_i}\bigg)_2},$
Substituting the values, we have
$=\frac{(6561\mathring{A})(1)^2\bigg(\frac{1}{2^2}-\frac{1}{3^2}\bigg)}{(2^2)\bigg(\frac{1}{2^2}-\frac{1}{4^2}\bigg)}=1215\mathring{A}$
$\therefore$ Correct option is (a).
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Concepts Used:
Atomic Spectra
The emission spectrum of a chemical element or chemical compound is the spectrum of frequencies of electromagnetic radiation emitted due to an electron making a transition from a high energy state to a lower energy state. The photon energy of the emitted photon is equal to the energy difference between the two states.
Read More: Atomic Spectra
Spectral Series of Hydrogen Atom
Rydberg Formula:
The Rydberg formula is the mathematical formula to compute the wavelength of light.
\[\frac{1}{\lambda} = RZ^2(\frac{1}{n_1^2}-\frac{1}{n_2^2})\]Where,
R is the Rydberg constant (1.09737*107 m-1)
Z is the atomic number
n is the upper energy level
n’ is the lower energy level
λ is the wavelength of light
Spectral series of single-electron atoms like hydrogen have Z = 1.
Uses of Atomic Spectroscopy:
- It is used for identifying the spectral lines of materials used in metallurgy.
- It is used in pharmaceutical industries to find the traces of materials used.
- It can be used to study multidimensional elements.