22.4 Energy Levels in Atoms and Line Spectra


2026 📋 Syllabus Objectives

By the end of this topic, you should be able to:

  1. Understand that there are discrete electron energy levels in isolated atoms (e.g. atomic hydrogen)
  2. Understand the appearance and formation of emission and absorption line spectra
  3. Recall and use the equation: hf = E₁ – E₂

1. Discrete Electron Energy Levels in Atoms

What is an energy level?

Inside every atom, there are tiny particles called electrons that exist around a central nucleus. These electrons do not just float around anywhere — they are only allowed to exist at certain fixed distances from the nucleus. Each of these allowed positions is called an energy level.

Think of it like floors in a building. An electron can stand on the ground floor, the first floor, the second floor, and so on — but it cannot stand between floors. It must be on one floor or another. This is what we mean when we say energy levels are discrete — they are separate, specific, and not continuous.

💡 Key idea: Electrons in atoms can only have certain specific amounts of energy — not any random amount. These fixed energy amounts are the energy levels.


How are energy levels represented?

Energy levels are drawn as horizontal lines, stacked on top of each other like shelves. Each shelf represents a different energy level. The energy values are always negative (this will be explained below).

Here is what the energy levels of atomic hydrogen look like:

LevelNameEnergy (eV)
n = 1Ground state−13.6 eV
n = 21st excited state−3.4 eV
n = 32nd excited state−1.5 eV
n = 43rd excited state−0.85 eV
n = 54th excited state−0.54 eV
Ionisation levelFree electron0 eV

💡 Why are the energies negative? When an electron is very far from the nucleus (at infinity), its energy is defined as zero. The electric field of the nucleus does work to pull the electron in closer, which lowers its energy. So electrons inside the atom have less than zero energy — that is why we use negative values. The closer the electron is to the nucleus, the more negative its energy, and the more tightly it is held.

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