Atomic Models & Energy Levels

You’ll be able to

Describe the Bohr model of quantized electron energy levels
Relate the energy of an emitted or absorbed photon to a transition between levels
Explain why atoms produce discrete line spectra

Electrons live on energy rungs

In the Bohr model of the atom, electrons can occupy only certain allowed orbits, each with a fixed, quantized energy level. An electron cannot have an energy in between — the levels are like rungs on a ladder, not points on a ramp. The lowest level is the ground state; higher ones are excited states. Energy levels are usually written as negative numbers (the electron is bound to the atom), approaching zero as the electron becomes free. This quantization is the central idea that classical physics simply does not contain.

Jumps make photons

An electron changes levels by absorbing or emitting a photon whose energy exactly matches the gap between the two levels: E_photon = |ΔE| = E_high − E_low. Absorbing a photon of just the right energy kicks the electron up; dropping down a level releases a photon of that energy. Because only specific gaps exist, only specific photon energies — and therefore specific wavelengths — are involved. A photon that does not match any gap simply passes by.

Photon energy from a transition

E_photon = E_high − E_low = h · f

The emitted or absorbed photon carries exactly the energy difference between the two levels. A larger energy gap means a higher-frequency (shorter-wavelength) photon.

Worked example

An electron drops from an energy level of −1.5 eV to a level of −3.4 eV. What is the energy of the emitted photon?

1.Emitted photon energy equals the size of the drop: E_photon = E_high − E_low.
2.Identify the levels: E_high = −1.5 eV, E_low = −3.4 eV.
3.Subtract: E_photon = (−1.5) − (−3.4) = −1.5 + 3.4 = 1.9 eV.

Answer: The emitted photon carries 1.9 eV — the electron released this energy as it fell to the lower level.

Checkpoint

An electron drops from a −1.5 eV energy level to a −3.4 eV level. What is the energy of the emitted photon?

Tip

When subtracting negative energy levels, watch the double negative: (−1.5) − (−3.4) = +1.9. The emitted photon’s energy is always the positive difference between the levels, regardless of their signs.

Checkpoint

Why do atoms emit light at only specific discrete wavelengths (a line spectrum) rather than a continuous range of colors?

On the exam

Line spectra are the fingerprint of quantization. Each element’s unique set of energy gaps gives it a unique pattern of spectral lines — the reason spectroscopy can identify the composition of distant stars.

Answer the 2 checkpoints as you read.