Bohr's model of the atom

The problem that Bohr had to solve

Rutherford's model has a small, heavy nucleus with the electrons moving round it, like planets round the Sun. It was a great step, but it had a serious problem.

An electron is a charged particle. A charged particle that moves in a circle should lose energy and send out light. If it did, the electron would spiral into the nucleus in a tiny fraction of a second, and every atom would collapse. But atoms do not collapse. The table in front of you has been stable for many years.

In 1913, the Danish scientist Niels Bohr gave a model that kept the nucleus but changed the rules for the electrons.

Bohr's ideas

1. An electron can move only in certain special orbits, called shells or energy levels. Other orbits are not allowed.
2. While an electron is in one of these orbits, it does not lose energy. So the atom does not collapse.
3. The shells are named K, L, M, N and so on, or by numbers $n = 1, 2, 3, 4$.
4. An electron can jump from one shell to another. To go to a shell farther from the nucleus, it must take in a fixed amount of energy. When it falls back, it gives out the same amount of energy as light.

The staircase picture

A good way to think of energy levels is a staircase. A person can stand on step 1 or on step 2, but not between the steps. In the same way, an electron can be in the K shell or in the L shell, but never between them.

The shell nearest to the nucleus, the K shell with $n = 1$, has the lowest energy. The energy rises as we go outward. An electron sits in the lowest shell that has room, as a ball rolls down to the lowest place it can reach.

To climb from one step to a higher one, you need energy. To climb from the K shell to the L shell, an electron needs a fixed amount of energy, no more and no less. When it falls back down, it gives out the same amount, and the atom shines.

You should find that a fall to the K shell gives out far more energy than a fall to the L shell, because the K level lies far below the others.

How many electrons can a shell hold?

Each shell can hold only a limited number of electrons. A shell with number $n$ can hold at most $2n^2$ electrons.

The next lesson shows the rules for filling the shells with electrons.

What the model explained

• Why atoms are stable. An electron in an allowed shell does not lose energy, so it does not fall into the nucleus.
• The colours of hot gases. Heat a salt of sodium in a flame, and the flame becomes bright yellow. Copper gives a green flame. Each jump of an electron gives out a fixed amount of energy, so each atom gives light of fixed colours. This is how scientists find which elements are in the Sun and in distant stars, from the colours of their light.

Later, other scientists improved the model again, because it works well for hydrogen but not for bigger atoms. Even so, the shell picture is the simplest way to show the electrons of an atom, and we use it throughout this book.

A picture of the sodium atom

Sodium has $11$ protons and $12$ neutrons in the nucleus, and $11$ electrons in three shells: $2$ in the K shell, $8$ in the L shell and $1$ in the M shell.

The atom is neutral, because the $11$ protons ($+11$) are balanced by the $11$ electrons ($-11$). The one electron in the outer shell is the one that sodium gives away when it forms a compound, and we study this in the chapter on bonding.

Rutherford and Bohr side by side

Practise with new numbers

Try it in Python

The program prints how many electrons each shell can hold, and the energy levels of hydrogen.

Common mistakes

• Thinking that electrons can stay between two shells. They can only be in a shell, or jump from one to another.
• Thinking that an electron in a shell gives out light all the time. It gives out light only when it falls to a lower shell.
• Mixing up the shell number and the number of electrons. The L shell is the second shell, with $n = 2$. It holds at most $8$ electrons.
• Thinking that the shells are real circles. The picture is a model. It is a good one, but electrons are not tiny balls on tracks.

Remember these

• Bohr: electrons move only in fixed shells, or energy levels, and do not lose energy in them.
• The shells are K, L, M, N, with $n = 1, 2, 3, 4$. They can hold $2$, $8$, $18$ and $32$ electrons.
• An electron jumps to a higher shell when it takes in energy, and gives out energy as light when it falls.
• The K shell has the lowest energy.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. Why does the atom not collapse in Bohr's model?

2. Which shell has the lowest energy?

3. What happens when an electron falls from the M shell to the K shell?

4. How many electrons can the N shell hold?