The Balmer Series in Hydrogen Atom Spectra

What is the formula to calculate the wavelength of the lines in the Balmer series?

a) 1/λ = R_H (1/2^2 - 1/n^2)

b) 1/λ = R_H (1/3^2 - 1/n^2)

c) 1/λ = R_H (1/4^2 - 1/n^2)

d) 1/λ = R_H (1/5^2 - 1/n^2)

Answer

The formula to calculate the wavelength of the lines in the Balmer series is: 1/λ = R_H (1/2^2 - 1/n^2)

The Balmer series is a set of spectral lines in the hydrogen atom that are emitted when electrons transition from higher energy levels to the second energy level. Each line in the series corresponds to a specific transition. The formula to calculate the wavelength of the lines in the Balmer series is given by:

1/λ = R_H (1/2^2 - 1/n^2)

In this formula, λ represents the wavelength, R_H is the Rydberg constant, and n is the principal quantum number of the energy level the electron transitions from.

For example, in the given data, the wavelength of the 1st line in the Balmer series is 656 nm. To find the wavelength of the 2nd line (n=3), we can calculate it using the formula. The limiting line in the Balmer series corresponds to the transition where n approaches infinity, resulting in a large wavelength value.