Question

Which of the following series of transitions in the spectrum of hydrogen atom falls in the visible region?

• A. Lyman series
• B. Balmer series
• C. Paschen series
• D. Brackett series

Answer 1

The correct option is B

Balmer series

Explanation for correct option

Option B

1. Based on many waves, there are spectrums like cosmic, gamma, x-ray, UV, visible light, infrared, microwave, and radio wave region. Only the wavelengths of visible light can be seen by the human eye which ranges from$380nmto780nm$.
2. There is 1 proton and 1 electron in the Hydrogen atom. Bohr in his atomic model gave the energy state of the orbitals of the atom and the spectral emission is based on Schrodinger’s equation.
3. Electrons tend to jump from higher energy levels to lower energy levels emitting energy in form of spectral emissions. The spectral lines are assembled to form the spectral series. There are 4 such series shown by Hydrogen named Lyman, Balmer, Brackett, and Paschen.
4. The Rydberg formula based on the energy differences and the wavelengths of the emitted photons is
   $${\displaystyle \frac{1}{\lambda }}=Z^{2}R\left({\displaystyle \frac{1}{{n_1}^2}}-{\displaystyle \frac{1}{{n_2}^2}}\right)$$
   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 Rydberg’s constant.
5. We can obtain different series 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}$.
6. Putting the values of R and Z, the values of the wavelengths can be found for different values of the energy levels and we observe the Balmer series starting from 656nm.
7. So in the spectrum of Hydrogen atoms falling in the visible region.

Explanation for incorrect option

Option A

1. We see the range of wavelength of the Lyman series starting from 121.6 nm toward shorter wavelengths and there is a decrease in the spacing between the lines as they reach the Lyman limit at 91.2 nm.
2. All the wavelength of the Lyman series falls in the Ultraviolet band.
3. Hence, option A is incorrect.

Option C

1. The wavelength range of the Paschen series starts from 1875nm.
2. All the wavelength of the Paschen series falls in the Infrared region of the electromagnetic spectrum.
3. Hence, option C is incorrect.

Option D

1. The wavelength range of the Brackett series starts from 4051nm.
2. All the wavelength of the Brackett series falls in the Infrared region of the electromagnetic spectrum.
3. Hence, option D is incorrect.

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