Question

Which one of the following series of transitions in the spectrum of hydrogen atom fall in the visible region?
A. lyman series
B. balmer series
C. paschen series
D. bracket series

Answer 1

Hint: The hydrogen spectrum comprises different series which have different energies associated with them. The energy can be linked to the wavelength which was given by Rydberg and the wavelength decides the regions of the spectrum.

Complete step by step solution:
-There are many waves that exist in this universe with different wavelengths and different frequencies. The waves with higher frequency have less wavelength and vice versa.
-Based on this, the spectrum is classified mainly as cosmic, gamma, x-ray, UV, visible light, infrared, microwave and radiowave region. The wavelength of visible light ranges from 380 nm to 780 nm. Only the wavelengths of these ranges can be seen by the human eye.
-Hydrogen atom consists of 1 proton and 1 electron. The energy state of the orbitals of the atom was given by Bohr in his atomic model and the spectral emission is based on Schrodinger’s equation.
-Electrons jump from higher energy level to lower energy level releasing energy in form of spectral emissions. The spectral lines are grouped together to form the spectral series. Hydrogen shows 4 such series named Lyman, Balmer, Brackett and Paschen.
-The energy differences and the wavelengths of the emitted photons is related by Rydberg formula as
\[\dfrac{1}{\lambda }={{Z}^{2}}R\left( \dfrac{1}{{{n}_{1}}^{2}}-\dfrac{1}{{{n}_{2}}^{2}} \right)\]
Where Z is the atomic number, n is the principal quantum number and the numbers 1 and 2 represent the lower and higher energy levels and R is the Rydberg’s constant.
-Different series are obtained by changing the values of n as 1,2,3 and 4 for hydrogen. The value of R for hydrogen is $1.09677$$\times$${{10}^{7}}{{m}^{-1}}$ .
-Putting the values of R and Z, we can find the values of the wavelengths for different values of the energy levels and by doing so, it is observed that the range of wavelengths for visible light is obtained in the Balmer series only.
-The range for Lyman series starts from 121 nm and decreases further, Balmer series starts from 656nm, Paschen series starts from 1875nm and Brackett series starts from 4051nm.

Therefore we see that the Balmer series falls under the visible region in the hydrogen spectrum and the correct option is B.

Note: The range of wavelengths for the ultraviolet region is between 100nm and 400nm and that of the infrared region lies between 760nm and 1000nm. As the value of n keeps on increasing, the value of wavelength keeps on decreasing.