Bohr Model Energy Level Calculator

The Bohr Model Energy Level Calculator calculates the energy change when an electron jumps between orbital shells in hydrogen-like atoms — a fundamental concept in atomic physics used to explain why atoms emit or absorb light at specific colors. Select your ion type (hydrogen, helium ion, lithium ion, etc.) and enter the initial energy level (n₁) and final energy level (n₂) to get the energy difference (ΔE) in eV, plus the emitted or absorbed photon's wavelength, frequency, and its spectral series name.

Principal quantum number of the initial energy level

Principal quantum number of the final energy level

Results

Energy Difference (ΔE)

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Initial Energy Level (E₁)

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Final Energy Level (E₂)

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Photon Wavelength (λ)

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Photon Frequency (ν)

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Spectral Series

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Frequently Asked Questions

What is Bohr's atomic theory?

Bohr's atomic theory describes electrons orbiting the nucleus in fixed energy levels. Electrons can only exist in specific quantized orbits, and they emit or absorb photons when transitioning between these energy levels.

How to calculate energy in nth Bohr's orbit?

The energy of an electron in the nth Bohr orbit is calculated using En = -13.6 × Z²/n² eV, where Z is the atomic number and n is the principal quantum number. The negative sign indicates the electron is bound to the nucleus.

How many energy levels does hydrogen have?

Theoretically, hydrogen has infinite energy levels (n = 1, 2, 3, ...). However, practically observable transitions typically involve the first few levels, with n=1 being the ground state and higher levels representing excited states.

What is the relationship between frequency and energy in the Bohr model?

The energy of a photon is directly proportional to its frequency: E = h×ν, where h is Planck's constant. When an electron transitions between energy levels, the energy difference equals the photon energy emitted or absorbed.

How do hydrogen-like atoms differ from hydrogen?

Hydrogen-like atoms are ions with only one electron but different nuclear charges (Z > 1). They follow the same Bohr model equations but with Z² scaling, making their energy levels more tightly bound than hydrogen.

What are the main spectral series in hydrogen?

The main series are: Lyman (transitions to n=1, UV region), Balmer (transitions to n=2, visible region), Paschen (transitions to n=3, infrared), and Brackett (transitions to n=4, far infrared).

How is wavelength related to energy difference?

Wavelength is inversely related to energy difference through λ = hc/|ΔE|, where h is Planck's constant and c is the speed of light. Higher energy transitions produce shorter wavelengths (bluer light).

What happens when an electron absorbs or emits a photon?

When an electron absorbs a photon, it jumps to a higher energy level (excitation). When it emits a photon, it falls to a lower energy level. The photon energy must exactly match the energy difference between levels.