Question

What is the longest wavelength present in the Balmer series of hydrogen?

Answer 1

The Balmer series

• When electrons transition occurs from a higher energy level to a lower energy level, a series of spectral emission lines occur. The visible lines in the spectrum of hydrogen are known as the Balmer series.
• Johann Balmer related these wavelengths of emitted light $\left(\lambda \right)$, speed of light (C), higher energy level (m), and lower energy level (n) using the Balmer formula as $\lambda =C\left(\frac{m^2}{m^2-n^2}\right)$
• Later Johannes Rydberg reformed the formula by introducing Rydberg constant (R) as $\lambda =R\left(\frac{1}{{n_f}^2}-\frac{1}{{n_i}^2}\right)$.

Longest wavelength in the Balmer series:

• $6563A^{\mathit{0}}$ is the longest wavelength in the Balmer series of hydrogen. The longest wave emission occurs when electron transits from energy level n=3 to n=2.
• Therefore according to the formula the wavelength $\left(\lambda \right)$, can be calculated as a function of the Rydberg constant (R) and energy levels s

$$\begin{gathered} \lambda =R\left(\frac{1}{{n_f}^2}-\frac{1}{{n_i}^2}\right) \\ =1.097x{10}^{-7}\left(\frac{1}{2^2}-\frac{1}{3^2}\right) \\ =1.097x{10}^{-7}\left(\frac{5}{36}\right) \\ =6.536x{10}^{-7}m \\ =6536x{10}^{-10}m \\ =6566A^0 \end{gathered}$$

The longest wavelength present in the Balmer series of hydrogen is $6566A^0$.