Why Do Atoms Have Discrete Energy Levels?

• Lowest level
• A higher level
• Electron sitting at one level
• Gap between levels, no state there

What you will learn

• Explain what discrete energy levels mean.
• Describe what happens when an electron changes level.
• State what the Bohr model explains and what it leaves open.

Before you start

You only need to know that an atom has a nucleus and electrons. No formulas are needed.

What do discrete energy levels mean?

They mean an electron can have only certain energy values. The Physics Book at Georgia Tech says that in the Bohr model electrons can only exist in discrete energy levels, which are quantized. It compares this with stepping up a staircase: you can stand on a step, not in the space between two steps.

In the Bohr model, the orbits are assigned exact radii. This is an older illustrative model, rather than a claim that real electrons occupy only those circular tracks.

• Nucleus at the centre
• An allowed orbit
• Dashed orbit excluded in the Bohr model

What happens when an electron changes level?

An electron jumps from one orbit to another when it gains or loses energy. The Georgia Tech page covers both directions. To go to a higher level, the electron needs an input of energy. When it drops to a lower level, it releases the difference as a photon.

In the atomic emission process considered here, an electron moves to a lower energy level and emits a photon. In both directions the quantized energy equals the difference between the energies of the two orbits. Since only certain differences are possible, energy can only be absorbed or emitted in specific quanta.

• Higher energy level
• Electron jumping to the lower level
• Emitted photon

Why are there only those levels?

The electron's wave nature and its confinement in an atom allow only certain energy states. OpenStax's discussion of matter waves and quantization explains this with a closed-loop wave model: the wave must join back onto itself after a circuit. Constructively interfering parts form an allowed wave pattern.

Picture a string bent into a loop. If a whole number of wavelengths fits around it, the end matches the beginning. With a leftover fraction, the parts do not match. Only matching patterns are allowed in this model. Wavelength is related to electron momentum, so restricting the wave patterns also restricts energy: separate levels result instead of a continuous range.

OpenStax notes that modern quantum theory replaces definite orbits with a probability cloud. Circular drawings help explain a wave condition; they are not real electron tracks. The Georgia Tech page also distinguishes the Bohr model's success from its limits: it predicts hydrogen's energy levels but does not itself explain why those levels are allowed.

• Matching wave pattern
• Mismatched wave pattern

Real-world example

• Three energy levels
• Three downward jumps of different lengths
• Dark strip of the spectrum
• Three bright lines, each matching one jump

Think of a vending machine that accepts only fixed coins. You cannot pay an amount between two denominations. Each coin you insert moves the total from one level to another. An atom also changes energy in steps that already exist.

Ask yourself: if a new step appeared between two old ones, would the light emitted when an electron drops gain a new line? The question shows that spectral lines depend on the steps.

Common misunderstandings

An electron does not circle the nucleus like a planet around the Sun. The Bohr model treats electrons as having a definite radius and momentum, and the Georgia Tech page says this violates the uncertainty principle.

The Bohr model is useful but incomplete. It predicts hydrogen energy levels; the wave model adds an explanation of why only certain states are allowed.

In an atomic transition, the photon energy matches the difference between the two levels. This does not give every photon in nature a single shared set of allowed energies.

Frequently asked questions

Can an electron sit between two energy levels?

Not in the Bohr model. Electrons exist only in discrete energy levels, like standing only on the steps of a staircase.

How is a photon produced?

A photon is produced when an electron moves to a lower energy level. An input of energy is required to go the other way.

Has the Bohr model explained why levels are discrete?

Not completely. Bohr assumed the angular momentum values, and his analysis offered no reason why only certain levels were allowed.

Summary

• Electrons in atoms have only discrete energy levels.
• A jump to a lower level emits a photon, and the emission spectrum is made of separate lines.
• Matching wave conditions allow only certain states; Bohr circles are an older model, not real trajectories.