Physics · Modern Physics

Bohr Model

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Wrap-up

What you learned

Recommended next: Open concept testCheck whether the core ideas are ready without leaving this concept.
Read next: Photoelectric EffectUse photon energy in a different quantum experiment.

Key takeaway

Hydrogen's Bohr levels are quantized, so only certain transition gaps and wavelengths are available.
Holding the lower level fixed creates named series such as Lyman, Balmer, and Paschen.
Within one series, higher starting levels crowd toward a wavelength limit because the upper energies bunch together.
Matching emission and excitation between the same two levels use the same wavelength magnitude.
Bohr is a bounded hydrogen model that points toward, but does not replace, fuller quantum mechanics.

Common misconception

Do not read the orbit picture as permission for any radius or any color. On this page the only honest transitions are the allowed hydrogen level gaps, and the literal-orbit model has a limited scope.

In the Bohr model, only specific energy levels are allowed, so only specific photon energies and wavelengths appear.

Carry the hydrogen story forward

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de Broglie Matter Waves

Use one compact matter-wave bench to see how particle momentum sets wavelength, why heavier or faster particles get shorter wavelengths, and how whole-number loop fits form a bounded bridge toward early quantum behavior.

Line evidence behind BohrModern Physics

Atomic Spectra

Link discrete emission and absorption lines to allowed energy-level gaps with one compact ladder-and-spectrum bench that keeps transitions, wavelengths, and mode changes tied together.

Probabilistic decay branchModern Physics

Radioactivity and Half-Life

Use one compact decay bench to see why each nucleus decays unpredictably, why large samples still follow a regular half-life curve, and how to read remaining-count graphs honestly.

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Reference and support

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Equation snapshotLevel gap to wavelength snapshot · Allowed transition energyShow 3 equations

Pick two allowed hydrogen levels first. The energy gap sets the photon wavelength; holding the lower level fixed creates a named series, and reversing the jump keeps the wavelength magnitude fixed.

Level gap to wavelength snapshot
$E_{n} = - \frac{13.6 eV}{n ^{2}}$
Hydrogen's allowed Bohr energies get closer together as n increases.
Allowed transition energy
$Δ E = 13.6 eV (\frac{1}{n _{f}^{2}} - \frac{1}{n _{i}^{2}})$
This gives the size of the allowed energy gap between two hydrogen levels.
Gap to wavelength
$λ = \frac{h c}{Δ E}$
Once you know the gap, you know the photon wavelength: larger gaps give shorter wavelengths.

Why it behaves this way

Explanation

In the Bohr model of hydrogen, the electron is allowed to occupy only certain energy levels. That means it can change energy only by certain amounts, so hydrogen emits or absorbs specific wavelengths instead of a continuous rainbow. The model is historically important because it links observed line spectra to quantized energy levels, even though modern quantum mechanics gives the fuller picture.

On this page, the radius map, energy ladder, line strip, and spectrum graph all describe the same live transition. When you change the upper or lower level, the selected jump, wavelength, series family, reverse-excitation case, and worked-example readouts update together.

Key ideas

01In the Bohr model for hydrogen, the allowed energies follow E_n = -13.6 eV / n^2, so only certain transition gaps are possible.

02Keeping the lower level fixed groups the lines into named series such as Lyman, Balmer, and Paschen.

03Within one series, increasing the starting level makes the lines crowd toward a series limit because the upper energy levels get closer together.

04The Bohr model is useful for understanding hydrogen spectral lines, but it is not the final quantum-mechanical description of atoms.

Worked examples

Live Bohr checks

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Frozen walkthrough

Step through the frozen example

Frozen walkthrough

Read each result from the same live bench. The level pair, energy gap, wavelength marker, graph, and overlays are all describing the same transition.

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Example 1 of 2

Frozen valuesUsing frozen parameters

For the current transition 3 -> 2, what photon energy and wavelength match this jump?

n_{i}

Upper level

n_{f}

Lower level

Δ E

Transition energy

1.89 eV eV

λ

Photon wavelength

656.39 nm nm

1. Read the active level pair

The bench is currently showing 3 -> 2, so the electron changes between n = 3 and n = 2.

2. Read the energy gap

That allowed hydrogen gap is 1.89 eV on the live ladder and readout card.

3. Convert the gap to a wavelength

Using

λ = h c /Δ E

, this jump gives 656.39 nm in the Visible.

Current transition

Δ E = 1.89 e V, λ = 656.39 nm, V i s ib l e

This Balmer transition lands in visible red, so the line sits inside the same wavelength window the graph and strip highlight together.

Common misconception

Use this only when you want to pressure-test a mistaken intuition.

If the electron circles the nucleus, it should be able to drop between any two radii and produce any color.

In the Bohr model, only specific energy levels are allowed, so only specific photon energies and wavelengths appear.

Modern quantum mechanics replaces the literal orbit picture, but quantized energy levels still explain why hydrogen has discrete spectral lines.

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Modern Physics

Bohr Model appears later in this track, so it is cleaner to start from the beginning first.

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