Rydberg Equation Calculator

Created by Dominik Czernia, PhD
Reviewed by Bogna Szyk and Steven Wooding
Last updated: Jan 18, 2024


Our Rydberg equation calculator is a tool that helps you compute and understand the hydrogen emission spectrum. You can use our calculator for other chemical elements, provided they have only one electron (so-called hydrogen-like atom, e.g., He⁺, Li²⁺ , or Be³⁺).

Read on to learn more about different spectral line series found in hydrogen and about a technique that makes use of the emission spectrum. In the below text, you will also find out what the Rydberg formula is.

💡 Check our hydrogen energy levels calculator if you want to compute the exact energy levels of a hydrogen-like atom.

Hydrogen emission spectrum

We know from the Bohr model that electron orbits around the nucleus only at specific distances, called energy levels n (n > 0 and is an integer).

When an electron drops to a lower orbit (n decreases), it emits an electromagnetic wave (photon) of a particular wavelength corresponding to the change of the electron's energy.

There are many possible electron transitions in an atom, and the collection of those transitions makes up an emission spectrum, which is unique for each element. In hydrogen, we obtain different series:

  • Lyman series, when an electron goes from n ≥ 2 to n = 1 energy level;

  • Balmer series, when an electron goes from n ≥ 3 to n = 2 energy level;

  • Paschen series, when an electron goes from n ≥ 4 to n = 3 energy level;

  • Brackett series, when an electron goes from n ≥ 5 to n = 4 energy level;

  • Pfund series, when an electron goes from n ≥ 6 to n = 5 energy level; and

  • Humphreys series, when an electron goes from n ≥ 7 to n = 6 energy level.

💡 To learn more about Bohr's model of the atom, check out our bohr model calculator.

Rydberg formula

The specific wavelengths of emitted light could be predicted with the following Rydberg formula:

1λ=RZ2(1n121n22),\frac{1}{\lambda} = RZ^2\left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right),

where:

  • λ\lambda – Wavelength of emitted light (in a vacuum);
  • ZZ – Atomic number (for hydrogen, Z=1\small Z = 1);
  • n1n_1 – Principal quantum number of the initial state (initial energy level);
  • n2n_2 – Principal quantum number of the final state (final energy level); and
  • RR – Rydberg constant for hydrogen R1.0973×107 m1\small R ≈ 1.0973 \times 10^7\ \rm m^{-1}.

In the advanced mode of our Rydberg equation calculator, you can compute the frequency and energy of the emitted electromagnetic wave. If you want to know how to convert wavelength to energy or frequency, check our photon energy calculator.

Spectroscopy

The study of the interaction between matter and an electromagnetic wave is called spectroscopy. It is a very helpful technique currently used in many areas of science. We can distinguish three main types of spectroscopy:

  • Emission spectroscopy in which we measure the energy of photons released by the material. Emissions can also be induced by other sources, e.g., flames, sparks, or electromagnetic waves. Our Rydberg equation calculator is dedicated to this type of spectroscopy.

  • Absorption spectroscopy occurs when we pass photons through the material and observe which photon's energies were absorbed.

  • Reflection spectroscopy in which we determine how incident photons are reflected or scattered by the material.

FAQ

How do I find frequency using Rydberg equation?

To determine the frequency using the Rydberg equation,

  1. You first need to determine the wavelength(λ):
    1/λ = R × Z2 × (1/n12 - 1/n22)

  2. This equation gives you 1/λ.

  3. You can determine the reciprocal and have λ.

  4. Then, substitute the value in the frequency formula.

    Frequency = 299792458 / λ

  5. So, divide the obtained wavelength by the speed of light, and you have the frequency.

Is the Rydberg equation only for hydrogen?

In principle, the Rydberg equation in its true form only determines the wavelength of spectral lines for hydrogen. That being said, the equation can be modified to compute for other hydrogen-like atoms. The most important change would be the Rydberg constant for the required atom.

But don't go thinking you can do this for the entire periodic table. This modification only works for isoelectric atoms, like He and Li.

What is the value of Rydberg constant for hydrogen?

The value of the Rydberg constant for hydrogen is given as:

R≈1.0973×107 m−1.

In atomic physics, Rydberg's constant refers to the energy level of hydrogen and other hydrogen-like atoms.

What is the wavelength when hydrogen electron jumps from 4th to 2nd level?

The wavelength of the spectral lines of hydrogen for the jump from 4th to 2nd energy level is 486 nanometers. You can determine it using the formula:

1/λ = R × Z2 × (1/n12 - 1/n22)

Substituting the values:

1/λ = 1.0973×107 × 12 × (1/42 - 1/22)

1/λ = 1.0973×107 × 1 × (1/16 - 1/4)

1/λ = 1.0973×107 × (0.0625 - 0.25)

1/λ = 1.0973×107 × -0.1875

1/λ = - 2056875

λ = -1/2056875

λ = 4.86 ×10-7

λ = 486 nm

Dominik Czernia, PhD
Atomic number
Initial state
Final state
Wavelength
nm
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