In this explainer, we will learn how to describe and identify energy levels in atoms and determine the number of electrons each energy level can contain.

More than years ago, Niels Bohr proposed that the atom is a positively charged nucleus with orbiting negatively charged electrons. He stated that the negatively charged electrons occupy discrete energy levels as they rotate about the central atomic nucleus at very high speeds.

### Definition: Energy Levels

Energy levels are regions around the nucleus in which electrons move according to their energies.

Atoms have the lowest energy levels closest to the central nucleus and higher energy levels further away. Scientists use a single capital letter for each different energy level. A single capital letter K is for the lowest energy level, and capital letters like L and M are used for energy levels further from the nucleus.

The energy of a level depends on its distance from the nucleus. Levels tend to have a low energy state when they are close to the center of the atom and a higher energy state when they are further apart. Level K is closest to the central nucleus and has the lowest energy state of all levels. Levels L and M are further from the nucleus and have higher energy states.

### Example 1: Identifying Letters That Represent Energy Levels

Which of the following letters is **not** used to represent an energy level?

- M
- N
- L
- K
- I

### Answer

Scientists use single capital letters to represent the seven lowest energy levels in an atom. For example, they use a capital K and a capital L for the first and second lowest energy levels. They also use a capital M and a capital N for the third and fourth lowest energy levels. However, the capital letter I does not represent any of the seven lowest energy levels. So, E must be the answer.

Energy levels cannot all hold the same number of electrons. Some energy levels can hold a maximum of two electrons, while others can have several times more. The expression describes the maximum number of electrons in any energy level. This expression uses the symbol for level order.

Let us use the expression to determine the maximum number of electrons in the first (K) energy level. We should start by stating that the maximum number of electrons is equal to the expression :

We should then replace the symbol with the number one:

We can then square the number one and multiply it by the number two to determine the maximum number of electrons in energy level K:

The calculation shows that the lowest energy level can contain two electrons. We could similarly replace with the number three to determine how many electrons can stay in the third (M) energy level. We could even replace with 4 to determine the maximum number of electrons that can fit in the fourth (N) energy level.

### Equation: The Maximum Number of Electrons in an Energy Level

The following table shows how we can use the expression to determine the maximum number of electrons for the first four energy levels. We first write the level order and then square this number. We then finish by multiplying this squared number by two.

Level Symbol | Level Order () | Maximum Number of Electrons | ||
---|---|---|---|---|

K | 1 | 1 | 2 | 2 |

L | 2 | 4 | 8 | 8 |

M | 3 | 9 | 18 | 18 |

N | 4 | 16 | 32 | 32 |

The maximum number of electrons changes dramatically from one energy level to the next. The first energy level can contain 2 electrons, and the third and fourth levels can hold up to 18 and 32 electrons. Mathematicians would describe the increase as exponential. Scientists do not ordinarily apply this equation to levels higher than the fourth one. Atoms will ordinarily split if they have more than 32 electrons in an energy level, as they have too many protons to be stable.

### Example 2: Determining the Maximum Number of Electrons That Can Stay in the Third Lowest Energy Level

What is the maximum number of electrons that can occupy energy level X, shown in the diagram?

### Answer

Scientists use the expression to determine the maximum number of electrons that can occupy an energy level. The symbol in this expression represents level order.

The question requires us to determine how many electrons can stay inside the energy level with . We can calculate the answer if we write the expression and replace the symbol with 3:

The result of this calculation is as shown:

The equations show that the energy level with can contain eighteen electrons. The answer to this question is 18 electrons.

The electrons of an atom tend to fill all the lowest energy levels first and the higher ones after that. This order of filling gives the electrons the lowest possible energy state. We can understand this point if we consider a helium atom first and a lithium atom second.

The figure shows the electrons of the helium atom. The helium atom electrons have the lowest possible energy state because they fill the lowest energy level (K). The electrons would have a higher energy state if either one moved to a different energy level.

The lithium atom is slightly different because it has three electrons. It has too many electrons for energy level K, and one electron must stay in a different energy level. The lithium atom electrons have the lowest possible energy states because two are in energy level K and the other is in L.

Atoms are in the ground state when all their electrons are in the lowest possible energy states. For example, helium is in the ground state when it has both electrons in energy level K. Also, lithium is in the ground state when it has two electrons in energy level K and one in level L.

### Definition: Ground State

The ground state is the lowest possible energy state of an atom.

### Example 3: Identifying the Ground State for an Atom with Two Electrons

Which of the diagrams shows the ground state for an atom that contains two electrons?

### Answer

The ground state is the lowest possible energy state of an atom. The atom in question has a total of two electrons. So, it is in the ground state if both its electrons are in the lowest energy level, energy level K. Choice A is the answer because it has two electrons in energy level K.

Electrons will tend to stay in the ground state. They will usually only move to a higher energy level if they absorb a quantum with the right energy. The quantum should have an energy state that matches the energy difference of the high and low energy levels.

### Definition: Quantum

A quantum is a unit or packet of energy.

### Example 4: Calculating How Much Energy Is Needed to Promote an Electron from Energy Level K to L

The diagram below shows the energy levels and their values for an atom containing a single electron. How much energy does an electron need to move from the K level to the L level?

### Answer

An electron can move to a higher energy level if it gains a quantum with the right energy. The quantum must have an energy state that matches the energy difference of the high and low energy levels. So, we can determine the energy difference of levels K and L to determine the answer:

The result of this calculation is as shown:

The electron will be promoted from level K to level L if it gains 10.2 energy units. The answer must be 10.2 energy units.

Excited state atoms tend to be very unstable, and they do not stay excited for a very long time. They tend to rapidly emit any absorbed energy and return to a stable ground state. Scientists call this process the deexcitation of an unstable atom.

### Definition: Excited State Atoms

Excited state atoms do not have all their electrons in the lowest possible energy states.

Atoms do not have an overall electric charge because they have an equal number of protons and electrons. For example, the hydrogen atom is neutral, as it has one positively charged proton and one negatively charged electron. The helium atom is similarly electrically neutral since it has two protons and two electrons.

### Example 5: Determining the Number of Protons in an Atom with Six Electrons

An atom contains 6 electrons. How many protons does the nucleus of the atom have?

### Answer

All atoms are without an overall electric charge because they have an equal number of positively and negatively charged particles. They all have the same number of protons and electrons. The atom in question has six negatively charged electrons. So, it must have six positively charged protons. The answer to this question is 6 protons.

Let us summarize what we have learned in this explainer.

### Key Points

- Electrons tend to stay in energy levels as they move around the central nucleus.
- Scientists use a single letter to represent an energy level.
- The expression determines the maximum number of electrons for an energy level.
- Scientists do not ordinarily apply the expression to levels higher than the fourth one.
- Atoms are in the ground state when all their electrons are in the lowest possible energy states.
- Electrons can be promoted from a low level to a higher one when they absorb an appropriate amount of energy.
- Atoms are without electric charge, as they have an equal number of protons and electrons.