What is the difference in energy between the second and third electron energy levels of a hydrogen atom?

In this explainer, we will learn how to determine whether an electron shell of an atom is filled and which electron transitions are possible in a given atom.

An atom is made up of three different types of particles: protons, neutrons, and electrons. The neutrons and protons together make up the nucleus, while the electrons are outside of it. The diagram below shows an atom.

The pink dot in this diagram represents the nucleus as a whole, and the blue dots around it are electrons. This diagram, and all subsequent diagrams, are not to scale: electrons are much smaller than atomic nuclei, and the distance between them is greater than what would fit on the page.

For the sake of simplicity, these diagrams are electrically neutral unless otherwise stated. This means that for every electron there will be a proton, so you will be able to determine which element the atom is by comparing the electrons to the atomic number. For example, the above diagram has 2 electrons, so it is the element with atomic number 2, helium.

Let’s look at an example.

The diagram shows electrons in different electron shells in an atom. The atom is electrically neutral. What element is this an atom of?

Answer

This atom is electrically neutral, meaning that for every electron, there is a proton. There are 3 electrons, which means the atom has 3 protons, so the element has an atomic number of 3.

Looking at the periodic table, lithium has atomic number 3.

So this atom is lithium.

If instead of being electrically neutral, the atom in the example above had a charge of −1, then this would mean that it has one more electron than it has protons. Since there are three electrons, this means it would have two protons, making it helium instead.

In these diagrams, the electrons are seen to be in a ring around the nucleus. These rings are actually very specific and represent which shell the electrons are in. Each shell, also called energy level, can only handle a certain amount of electrons before having to move into an outer shell, as shown in the table below.

Electron shells are also called electron energy levels because the energy of the electrons within them changes from shell to shell. The electrons in the innermost shell are the least energetic, and those in the outermost shell are the most energetic.

Let’s look at an example.

The diagram shows electrons in different electron shells in an atom. All of the first four electron shells in the atom are filled.

1. Which of the electron shells contains the most electrons?
2. Which of the electron shells contains the fewest electrons?

Answer

Part 1

The shell number tells us how close the shell is to the nucleus. Shell 1 is the nearest, and shell 4 the furthest away. We can count the individual electrons to determine how many there are, but we can also see that as the shells go out more, the number of electrons in each increases as well.

The innermost ring, shell 1, contains 2 electrons. The next out, shell 2, contains 8; shell 3 has 18; and shell 4 has 32.

The electron shell that contains the most electrons is shell 4.

Part 2

The electron shell that contains the fewest electrons is the one closest to the nucleus, shell 1.

Usually, the electrons occupy the lowest energy level, neatly filling the shells from the innermost outward. When all of an atom’s electrons fill the lowest energy levels possible, we say the atom is in a ground state.

It is possible to make specific electrons temporarily have a higher energy level by exposing them to light. When electrons are in a higher energy level than the ground state, we say they are in an excited state. This means that it is possible for an electron to be in a higher shell before a lower energy level is filled up completely. The diagram below shows a neutral helium atom in both the ground and an excited state.

Let’s look at an example.

The diagram shows an electrically neutral neon atom. How many of the electrons in the atom are in excited states?

Answer

Let’s start by counting the total number of electrons and considering how many would be in the ground state. There are 2 in the first energy level, 6 in the second, and 2 in the third. There are a total of 10 electrons.

To be in the ground state, the 10 electrons must first fill the innermost shell, which can hold 2. So we have 8 electrons left.

The 8 will completely fill the second energy level, so in ground state, there should be no electrons in the 3rd shell. We see that there are 2 there though, so those 2 electrons in the 3rd shell must be excited.

There are 2 electrons in excited states, the ones in the third energy level.

When there are no excited electrons, energy levels fill up innermost to outermost. This means that before the second shell can begin being filled, it must have a full first shell.

Shells are not full if they do not hold the maximum number of electrons allowed in their shell. This means that if the 1st shell only has 1 electron, it is unfilled, since it can fit a maximum of 2.

Let’s look at an example.

The diagram shows electrons in different electron shells in an atom. The outermost shell is unfilled. How many more electrons can the atom have in its outermost shell?

Answer

When the question says outermost shell, it only means the outermost shell that currently has electrons in it. This means we are not looking to fill the third or fourth shell.

We know that the first shell can hold 2 and the second shell can hold 8. Looking at this diagram, the first shell is full, but the second shell only contains 7 electrons. It can fit exactly 1 more electron before becoming full.

The answer is 1 electron.

In order to become excited, an electron can absorb a photon, which is a particle of light. The energy of the photon is transferred to the electron, causing it to move up to a different energy level. Higher energy photons make the electron transition into higher energy levels.

To transition between two specific energy levels, the energy of the photon needs to be equal to the difference in energy between the energy levels. The diagram below shows a photon with an energy equal to the difference between the 1st and 3rd energy levels being absorbed by an electron.

The photon absorption causes the electron to transition from the 1st energy level to the 3rd. Electrons cannot stay in excited states for long though, and they decay back to the ground state after some time has passed, as seen in the diagram below.

A photon is emitted as the electron transitions from the third energy level back down to the first energy level. The energy of this photon that leaves is nearly identical to the photon that first excited it.

Let’s look at some examples.

The diagram shows a hydrogen atom. The electron shown transitions between two energy levels of the atom.

1. Which energy level is the electron initially in?
2. Which energy level does the electron transition to?

Answer

Part 1

The energy levels are counted from the inside out. We see that the electron is initially in the outermost level, the fourth ring from the center.

The electron is initially in the fourth energy level.

Part 2

The energy level the electron transitions to is indicated by the arrow and points to the second ring from the center.

The electron transitions to the second energy level.

Each of the following diagrams shows a hydrogen atom that is initially in an excited state. In each case, the electron transitions from a higher energy level to a lower energy level, emitting a photon. For which case is the energy of the emitted photon the greatest?

Answer

Electrons in higher energy levels have a higher energy than those in lower energy levels. When an electron transitions to a lower state, a photon is emitted, the energy of which is equal to the energy difference between the energy levels it is moving between.

This means that transitioning from a higher energy level to a ground state (such as from shell 3 to shell 1) results in a higher-energy photon compared to transitioning from a lower starting state (from 2 to 1).

In case A, we see a photon being emitted after the electron transitions from energy level 3 to energy level 1. The photon’s energy is also shown by its wavelength: shorter wavelengths mean more energy.

In case B, we see a photon being emitted as the electron goes from shell 2 to shell 1. This produces a long-wavelength photon with lower energy than case A, so it cannot be this one.

In case C, the electron transitions from energy level 4 all the way down to energy level 1, the furthest it can go. The photon emitted is of a short wavelength and a higher energy compared to case A, which only went from 3 to 1.

The case in which the emitted photon has the greatest energy is thus C.

Electrons that become excited and transition to higher energy levels must still obey the limit on how many electrons can fit into a particular shell.

Let’s look at an example.

The diagram shows an electrically neutral atom. If one of the electrons in the innermost shell were to absorb a photon and move into an excited state, which of the electron shells shown in the diagram could it move to?

Answer

An excited electron is able to move to any higher non-full energy level, so we need to find out which shells are full and which are not. Let’s recall the table that shows how many electrons are allowed in each energy level.

The electron that becomes excited is moving from the innermost shell, which we see has the full 2 electrons.

Shell 2, the second ring from the center, is full with 8 electrons. It is unable to fit anymore electrons.

Shell 3 only has 10 electrons, which is less than its full capacity of 18. Since shell 2 is full, the excited electron in shell 1 will have to jump past shell 2 directly into shell 3.

The answer is shell 3.

Let’s summarize what we have learned in this explainer.

• Electrons can be found around a nucleus and are arranged in shells, or energy levels.
• Electron energy levels are numbered, with higher levels having more energy.
• Electrons are in the lowest energy level possible, unless excited by a photon.
• Each energy level has a limit to the number of electrons it can hold, as shown in the table below.

  Shell/Energy Level	Electrons
  1	2
  2	8
  3	18
  4	32

• The greater the difference in energy levels, the greater the energy of the photon required to transition between those levels.