The **key difference** between Rydberg and Balmer formula is that **Rydberg formula gives the wavelength in terms of the atomic number of the atom whereas Balmer formula gives the wavelength in terms of two integers – m and n. **

Rydberg and Balmer’s formulas are important in determining the wavelength of photons emitted from the electron excitations. These formulas were developed for the hydrogen atomic spectrum. Therefore, these formulas are used with the Bohr model.

### CONTENTS

1. Overview and Key Difference

2. What is Rydberg Formula

3. What is Balmer Formula

4. Side by Side Comparison – Rydberg vs Balmer Formula in Tabular Form

6. Summary

## What is Rydberg Formula?

Rydberg formula is a mathematical expression which predicts the wavelength of light emitted from electron excitations in atoms. In other words, this formula finds the wavelength of photons that are emitted when an electron moves back to the ground state from its excited state. Rydberg formula was developed by the physicist Johannes Rydberg who attempted to derive a mathematical relationship between the wavenumbers of adjacent spectral lines of the hydrogen line spectrum. The formula is as follows:

**1/λ=RZ ^{2}(1/n_{1}^{2}-1/n_{2}^{2})**

Where, λ wavelength of the emitted photon, R is the Rydberg constant, Z is the atomic number of the atom that is being considered, and n_{1} and n_{2} are integers. Always n_{1} < n_{2}. Later, it was found that these two integers are related to the principal quantum number, which is involved in the photon emission.

However, this formula is applicable with the hydrogen atom and some other small atoms. But, when it comes to large and complicated atoms, Rydberg formula gives incorrect results because of the screening effect that arises due to the presence of multiple electrons (inner electrons are screened from outer electrons).

Moreover, by assigning different values to n_{1} and n_{2} integers, we can get the wavelengths corresponding to the different line series such as Lyman series, Balmer series, Paschen series, etc. When solving problems regarding the Rydberg formula, we have to use the values of principal quantum numbers for n_{1} and n_{2}. Since n_{1} < n_{2}, n_{1} is the quantum number of the energy level to which the electron moves while n_{2} is the quantum number of the energy level from which the excited electron is released.

## What is Balmer Formula?

Balmer formula is a mathematical expression that can be used to determine the wavelengths of the four visible lines of the hydrogen line spectrum. This formula was developed by the physicist Johann Jacob Balmer in 1885. He developed this formula using two integers: m and n. The formula is as follows:

**λ=constant(m _{2}/{m_{2}-n_{2}})**

However, this formula is entirely empirical. That means; it is not a formula that is derived from a particular theory. Moreover, the Balmer formula was true, but at the time of its development, there were less experimental data to prove that it is a true formula. Later, another physicist named Rydberg modified this formula, stating that Balmer formula has wide applicability, introducing the concept of wave number instead of wavelength.

## What is the Difference Between Rydberg and Balmer Formula?

Rydberg and Balmer’s formula are important formulas in chemistry. Actually, Rydberg formula is a derivative of the Balmer formula. Besides, the key difference between Rydberg and Balmer formula is that the Rydberg formula gives the wavelength in terms of the atomic number of the atom, but Balmer formula gives the wavelength in terms of two integers: m and n.

Below infographic summarizes the difference between Rydberg and Balmer formula.

## Summary – Rydberg vs Balmer Formula

Rydberg and Balmer’s formula are important formulas in chemistry. Rydberg formula is a derivative of the Balmer formula. The key difference between Rydberg and Balmer formula is that Rydberg formula gives the wavelength in terms of the atomic number of the atom, but Balmer formula gives the wavelength in terms of two integers, m and n.

##### Reference:

1. Helmenstine, Todd. “What Is the Rydberg Formula and How Does It Work?” ThoughtCo, Aug. 28, 2019, Available here.

##### Image Courtesy:

1. “HydrogenSpectrum” By Caitlin Jo Ramsey – Own work (CC BY-SA 3.0) via Commons Wikimedia

## Leave a Reply