Using Energy Level Diagrams (7.3.5) | AP Physics 2: Algebra Notes

AP Syllabus focus: 'Energy level diagrams visually represent atomic energy states and help show photon absorption, emission, and transitions in single-electron atoms.'

Energy level diagrams give a compact picture of how atoms store energy. In AP Physics 2, they are used to track allowed states and to interpret when photons are absorbed or emitted.

What Energy Level Diagrams Represent

An energy level diagram shows the allowed energies of an atom as separate horizontal lines. Each line stands for one possible atomic energy state, rather than a continuous range of energies.

Energy level diagram: A visual representation of the discrete allowed energy states of an atom.

For single-electron atoms, these diagrams are especially useful because the atom can be modeled as a nucleus with one electron in one of several allowed energy states. The electron cannot have just any energy. It must be in one of the listed levels.

The vertical placement of a line represents how much energy that state has relative to the others:

Lower lines represent lower-energy states.
Higher lines represent higher-energy states.
The spacing between lines represents the energy difference between states.

A key point is that the diagram does not show where the electron is located in space. It shows the atom’s allowed energies. A low line does not mean the electron is physically lower; it means the atom is in a lower-energy state.

The lowest allowed state is called the ground state. Any allowed state above it is an excited state.

Reading Changes Between Levels

When an atom moves from one allowed energy state to another, the change is shown by an arrow connecting two levels.

Transition: A change of an atom from one allowed energy level to another.

To interpret a transition, first identify the initial level and the final level. Then compare their energies. The atomic energy change is determined by the difference between the two levels.

$\Delta E = E_f - E_i$

$\Delta E$ = change in atomic energy, J

$E_f$ = final energy level, J

$E_i$ = initial energy level, J

If the final level is higher than the initial level, then $\Delta E$ is positive and the atom has gained energy. If the final level is lower, then $\Delta E$ is negative and the atom has lost energy.

In diagram questions, this simple comparison is often more important than doing a long calculation. The main task is usually to decide whether energy entered the atom or left it.

Absorption and Emission

Absorption

Absorption happens when the atom moves from a lower energy level to a higher one. On an energy level diagram, this is shown by an upward arrow.

When this occurs:

Hydrogen absorption infographic showing that only photons with specific wavelengths (energies) can promote the electron to higher allowed energy states. The figure ties each upward transition to a distinct missing (dark) absorption line, reinforcing the idea that the photon energy must match the energy gap exactly. Source

the atom gains energy
a photon provides that energy
the photon energy must match the energy gap between the two levels

An upward transition means the atom has taken in energy from its surroundings. In AP-style questions, this is commonly described as the atom absorbing a photon and becoming excited.

Emission

Emission happens when the atom moves from a higher energy level to a lower one. On an energy level diagram, this is shown by a downward arrow.

When this occurs:

the atom loses energy
a photon is produced
the photon carries away the energy difference between the two levels

A downward transition means the atom is moving to a more stable, lower-energy state. The emitted photon corresponds exactly to that energy drop.

Using the Size of the Energy Gap

The energy gap between two levels is one of the most important features of the diagram. A larger vertical separation means a larger energy difference. A smaller separation means a smaller energy difference.

This helps you compare transitions:

a larger gap corresponds to a more energetic absorbed or emitted photon
a smaller gap corresponds to a less energetic photon

Not every pair of levels is separated by the same amount.

Energy-level diagram for hydrogen showing multiple possible electron transitions grouped into spectral series (e.g., Lyman, Balmer, Paschen). The different arrow lengths represent different energy drops, illustrating why larger gaps correspond to higher-energy emitted photons (and, conversely, require higher-energy absorbed photons). Source

In many single-electron atom diagrams, the gaps get smaller as the levels get higher. That means different transitions can involve very different photon energies.

You should also remember that one arrow represents one specific transition between two allowed states. If several downward arrows can start from the same excited state, then several different emissions are possible, each with its own photon energy.

Some diagrams are drawn approximately, while others include exact numerical energy values. If values are given, use those values. If no values are given, focus on the relative order of levels and the relative sizes of the gaps.

How to Use Energy Level Diagrams on AP Physics 2 Questions

In AP Physics 2, energy level diagrams are mainly used as a reasoning tool. A typical question asks you to identify what happens during a transition, rather than to describe the full quantum model of the atom.

A good method is to:

identify the starting and ending levels
determine whether the arrow points up or down
decide whether the atom gained or lost energy
state whether the process is absorption or emission
compare the gap size if asked which transition involves the greater photon energy

For single-electron atoms, the diagram is especially clear because each line represents one allowed atomic energy state. This makes the diagram a simple way to connect the ideas of discrete energy states, photon transfer, and atomic transitions without needing a more advanced model.

FAQ

The zero of energy is usually chosen to mean the electron is completely free from the atom and infinitely far away.

A negative energy means the electron is still bound to the atom. The more negative the value, the more tightly bound that state is.

That top limit represents the point where the electron is no longer bound to the atom.

Above that point, the electron can have a continuous range of energies rather than a discrete set of allowed bound-state energies. On a diagram, this is sometimes shown as a boundary rather than a normal level line.

The symbol $n$ is a label for the allowed energy state in a single-electron atom.

Using $n$ values is useful when the question focuses on which state the atom is in, rather than on the exact numerical energy. If numerical energies are not shown, you can still compare levels by their order on the diagram.

A simplified diagram is often used to highlight only the states relevant to the question.

This helps you focus on:

the specific transition being discussed
the relative energy differences
whether absorption or emission occurs

The missing levels are not necessarily forbidden; they may just be omitted for clarity.

In single-electron atoms, the allowed energies are not evenly spaced.

As the levels get higher, the differences between neighboring energies usually become smaller. On a diagram, that makes the upper lines bunch closer together. This matters because transitions among higher levels often involve smaller energy changes than transitions involving the lowest levels.

Practice Questions

A single-electron atom is shown on an energy level diagram making a transition from a lower level to a higher level.

State whether the atom absorbs or emits a photon, and explain how the diagram shows this.

1 mark: States that the atom absorbs a photon.
1 mark: Explains that the transition is to a higher energy level, so the atom gains energy.

An energy level diagram for a single-electron atom has three allowed states: $E_1$ (lowest), $E_2$ , and $E_3$ (highest). The energy gap between $E_1$ and $E_2$ is smaller than the energy gap between $E_2$ and $E_3$ .

(a) Describe what happens when the atom transitions from $E_3$ to $E_2$ .
(b) Describe what happens when the atom transitions from $E_1$ to $E_2$ .
(c) Which transition involves the greater photon energy: $E_3 \to E_2$ or $E_2 \to E_1$ ? Justify your answer.

(a) 1 mark: States that a photon is emitted.
(a) 1 mark: Explains that the transition is downward to a lower energy level.
(b) 1 mark: States that a photon is absorbed.
(b) 1 mark: Explains that the transition is upward to a higher energy level.
(c) 1 mark: Correctly identifies $E_3 \to E_2$ as the greater photon energy because that energy gap is larger.

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