# Episode 507: Electron standing waves

Lesson for 16-19

- Activity time 50 minutes
- Level Advanced

You could extend the idea of electrons-as-waves further, to the realm of the atom.

Lesson Summary

- Demonstration: Melde’s experiment (20 minutes)
- Discussion: Electron waves in atoms (10 minutes)
- Demonstration: Standing waves on a loop (10 minutes)
- Student question: Electron standing waves (10 mins)

## Demonstration: Melde’s experiment

Episode 507-1: Standing waves – for electrons? (Word, 161 KB)

In this section we are going to introduce the idea of standing waves within an atom. It is therefore useful first to demonstrate standing waves on a stretched elastic cord. This is known as Melde’s experiment.

(A very simple alternative to the vibration generator is an electric toothbrush.)

Show that there are only certain frequencies at which standing wave loops occur.

## Discussion: Electron waves in atoms

The waves on the string are trapped

between the two fixed points at the ends of the string and cannot escape.

If the electron has wave properties and it is also confined within an atom we could imagine a sort of standing wave pattern for these waves rather like the standing waves on a stretched string. The electrons are trapped

within the atom rather like the waves being trapped

on a stretched string. The boundaries of these electron waves would be the potential well formed within

the atom.

This idea was introduced because the simple Rutherford model of the atom had one serious disadvantage concerning the stability of the orbits. Bohr showed that in such a model the electrons would spiral into the nucleus in about 1 × 10^{-10} s, due to electrostatic attraction. He therefore proposed that the electrons could only exist in certain states, equivalent to the loops on the vibrating string.

If your students have met the idea of angular momentum, you could tell them that Bohr proposed that the angular momentum of the electrons in an atom is quantised, in line with Planck's quantum theory of radiation. He stated that the allowed values of the angular momentum of an electron would be integral multiples of *h*2 π . This implied a series of discrete orbits for the electron. We can imagine the electron as existing as a wave that fits round a given orbit an integral number of times.

## Demonstration: Standing waves on a loop

The wire loop is a two dimensional analogy of electron waves in an atom. As it vibrates at the correct frequency, an integral number of waves fit round the orbit. These waves represent the electron waves in an atom.

## Student question: Electron standing waves

de Broglie waves can be imagined as forming standing waves which fit into an atom.

Episode 507-2: Electron standing waves (Word, 323 KB)