Bohr Model Calculator

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Dominik Czernia, PhD

Dominik Czernia

PhD, Institute of Nuclear Physics PAN

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Research Gate

Dominik Czernia, PhD, is a physicist at the Institute of Nuclear Physics in Kraków, specializing in condensed matter physics with a focus on molecular magnetism. He has led several national research projects, pioneering innovative approaches to novel materials for high technology. Passionate about making science accessible, Dominik has created various calculators, mostly in physics and math categories. In his free time, he enjoys family walks, city explorations, mountain hiking, and traveling everywhere by bike. See full profile

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Bogna Szyk and Adena Benn

Adena Benn

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Adena Benn is a Guyanese teacher with a degree in computer science who is always reading and learning. She loves problem-solving, everything tech, and working with teenagers. She has a passion for education and is especially interested in how children learn and the teaching methods that best suit their learning styles. She grew up on a farm in Pomeroon, Guyana, where she worked alongside her parents and siblings. As such, she is just as comfortable growing plants as teaching in the classroom. In her early life, she also gained expertise as a seamstress, which she learned from her mother. By grade 9, she had already acquired her dressmaker's certificate. Today she uses her skills to design many items for her family. In her free time, Adena loves to read, take long walks, write children’s stories and poetry, travel, or spend time with her family. See full profile

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The Bohr model calculator is a tool that can be used to compute the frequency of an electromagnetic wave that is emitted or absorbed at the transition of an electron in an atom.

In the text below, we explain the principles of the Bohr model and the definition of a hydrogen-like atom. Read on to investigate this theory further and learn about the relationship between frequency and energy.

Bohr model definition

We have known for a long time that nature is composed of a huge number of atoms. However, the discovery of the actual atomic structure took place relatively recently. The first theory that correctly describes the simplest atom, hydrogen, was proposed in 1913 and was called the Bohr Model. In this model, the atom consists of a nucleus surrounded by electrons, like the sun and planets in the solar system. The Bohr model definition comprises four points:

The electron is held in a circular orbit around the nucleus by Coulomb's force. You may read more about this in our Coulomb's law calculator.
Angular momentum of the orbiting electron is quantized. It means that the electron can only have specific energies on its orbital.
The electron can orbit without losing energy due to radiating, but only on a certain discrete set of distances from the nucleus. Every orbital is associated with specific energy, which is called an energy level.
The electron can jump between different energy levels by absorbing or emitting the photon — electromagnetic radiation. Its energy is determined by the difference between the initial and the final energy level.

Check out our photon energy calculator to find out how you can convert the frequency of the electromagnetic wave into energy.

Relationship between frequency and energy in the Bohr model

The Bohr model calculator computes the frequency of an electromagnetic wave emitted or absorbed by an electron with the following Bohr model equation:

ΔE = E2 - E1 = h × f

where:

E2 — Initial energy level of the electron;
E1 — Final energy level of the electron;
ΔE — Difference between those energies;
f — Frequency of absorbed/emitted electromagnetic wave; and
h — Planck's constant which equals h = 6.6261 × 10^-34 J⋅s.

When the final energy level is smaller than the initial energy level, the energy difference is ΔE > 0, and thus, the electron will emit the electromagnetic wave. Otherwise, when ΔE < 0, the electron needs to absorb the electromagnetic wave. Remember that the energy levels of the electrons bound to the atom are negative!

Hydrogen-like atoms

The Bohr model is a simplified theory that correctly describes atoms with only one electron orbiting around the nucleus (hydrogen-like atoms). The energy of the lowest orbit in the hydrogen atom is -13.6 eV, and the second lowest energy is -3.4 eV. You can check it with our hydrogen energy levels calculator.

The energy difference between those orbits equals ΔE = 10.2 eV, and it corresponds to the frequency f = 2466.3 THz ≈ 2.5 × 10¹⁵ Hz, which is astonishingly high! You can check this result with this Bohr model calculator.