In atoms, energy changes are not arbitrary. Electrons can move only between specific allowed states, so any absorbed or emitted photon must carry exactly the needed amount of energy.

Allowed Atomic Energy States

In quantum physics, an atom does not allow an electron to have just any energy. Instead, the atom has a set of allowed energy states, often called energy levels. Each state represents a specific total energy for the atom-electron system. Between those states, the AP Physics 2 model does not treat the atom as having stable intermediate energies.

This means atomic energy exchange is quantized.

Energy-level schematic showing discrete (allowed) states and the two possible photon-mediated transitions: absorption (upward jump) and emission (downward drop). The visual makes the “exact matching” idea concrete—each photon corresponds to one specific gap between two levels, not a continuum of energies. Source

The atom cannot gain or lose a random amount of energy and remain in a valid atomic state. Any change must connect one allowed state to another. Any such change is an energy level transition.

A transition is not a gradual slide through all possible values. The atom starts in one allowed state and ends in another. If the required energy is not transferred exactly, that particular transition does not occur.

The Exact Matching Requirement

For any transition, the key quantity is the difference between the initial energy and the final energy. That difference sets the exact amount of energy the atom must absorb or emit.

The sign of $\Delta E$ shows the direction of the change. If $E_f > E_i$, then the atom moves to a higher-energy state and must gain energy. If $E_f < E_i$, then the atom moves to a lower-energy state and loses energy. In either case, the photon involved must have an energy equal to the size of the gap, so $E_{photon} = |\Delta E|$.

This requirement follows from energy conservation. The atom and photon exchange energy in exact amounts, not approximate ones. A photon whose energy does not match an allowed gap cannot produce that transition in the basic AP model.

Why the current state matters

The same atom can respond differently to the same photon depending on which state the atom is already in. Suppose a photon has an energy equal to one particular gap from a lower state to a higher state. That photon can be absorbed only if the atom actually starts in the lower state connected by that gap.

This is why transition questions always depend on both the available energy levels and the atom’s initial state.

Hydrogen absorption infographic connecting electron transitions to specific absorbed wavelengths and the corresponding dark lines in the absorption spectrum (Balmer-series example). It reinforces that a photon is absorbed only when its energy matches an allowed energy-level gap, so the observed spectrum contains discrete lines rather than a continuum. Source

A photon that is a perfect match for one upward transition may fail to interact if the atom begins in a different state. Likewise, an excited atom can emit only the photon energies that match drops from its present state to lower allowed states.

Absorption Transitions

During absorption, the atom takes in a photon and moves to a higher allowed energy state. The incoming photon must provide exactly the energy needed for that upward jump. If the photon has too little energy, the atom cannot reach the higher state. If the photon has too much energy, the extra energy does not simply stay behind while the transition happens anyway.

More photons of the wrong energy do not fix the mismatch for a single ordinary transition. The central AP Physics 2 idea is that one photon must match one allowed energy difference. Therefore, absorption is selective: only certain photon energies can be absorbed from a given starting state.

Emission Transitions

During emission, the atom moves from a higher allowed state to a lower one. The atom’s energy decreases, and a photon carries away exactly that lost energy. Because the states are discrete, the emitted photon energy is also discrete.

If an atom has several lower states available, more than one downward transition may be possible.

Hydrogen energy-level diagram showing discrete levels and families of allowed transitions (Lyman, Balmer, Paschen series). Each arrow represents a specific energy drop, so each possible transition corresponds to a distinct emitted photon energy rather than a continuous range. Source

Each possible drop corresponds to its own exact photon energy. The atom does not emit a continuous range of energies between the allowed gaps; it emits only the energies associated with actual transitions.

An excited atom may not always drop to the lowest state in one step. It can transition in stages, but every stage still follows the same rule: the photon energy must equal the difference between the two states involved in that single step.

What AP Physics 2 Emphasizes

On this subtopic, the most important reasoning is to compare a photon’s energy with the differences between allowed atomic energy states. If there is an exact match, the transition is possible. If there is no match, the transition is not possible in the model.

• Absorption means the atom ends in a higher energy state.

• Emission means the atom ends in a lower energy state.

• The relevant quantity is the energy difference between states.

• The photon energy must match that difference exactly.

• Atoms do not absorb or emit arbitrary amounts of energy.

These ideas capture the central quantum feature of atomic transitions: atomic energies are restricted to allowed values, so energy transfer with light occurs only in specific, permitted amounts.