Sitting on a lot of desks around the country are mathematical calculators that never need batteries to power their computations so long as light is shining on them. When sunlight falls on a panel of bluish squares above the keys and display, the calculator works and electricity pulses though the digital chips to ponder the results of "1 + 1" or determine the value of 50%.

However, if that calculator is moved away from the window and into a box where it is only exposed to pure red light of a single frequency or wavelength, it suddenly stops working. Electricity no longer flows and all computations cease! Those bluish panels, when exposed to red light, can no longer provide a source of electrons.

Perhaps the red light is not strong enough?

It doesn't matter. The most powerful red light you can shine on a calculator cannot power it! Cranking up the intensity of the red light will only make the box and the machine hotter - it will not make the electricity flow.

Remove the red light and replace it with a violet or bluish light, and suddenly the calculator springs back into life and mathematics are at your finger tips once more. Not only that, but you can turn down the intensity of the violet-blue light to very faint levels, and the calculator will still work.

What is going on and what can this tell us about the properties of electrons?

Even cheap calculators these days are powered by what is called the photoelectric effect, a phenomenon first seen and studied in the last two decades of the nineteenth century.

Electric current is the movement of electrons along metal wires and through metal devices. Sometimes, however, the electrons can be made to "jump" into the air and leave the surface of the metal altogether.

This was observed happening in 1902 by the German physicist Philipp Lenard. When light was directed onto the surface of certain metals, it appeared that electrons were being dislodged from the surface of the metal and out into the surrounding space.

Light, it was known, contained radiant energy, so it was assumed that the light was passing some of this energy to the electrons buzzing around the atoms of the metal and ejecting those electrons out and far away from their host atoms. It seemed a reasonable assumption. It also seemed a reasonable assumption that the stronger and more intense the light source the more electrons would be affected and ejected.

Until Lenard started measuring.

In 1902 he made a series of very careful measurements of how, when and under what circumstances light would dislodge electrons from metal atoms. What he found surprised him and other physicists of the time.

First, there was a "threshold effect". Just like the calculator described above, when light with a frequency of about 5 x 10¹⁶ Hz (cycles per second) was shone on the metal - nothing happened, no matter how intense and bright a light it was.

But if the frequency of the light was increased to about 6 x 10¹⁶ Hz, then electrons started flying off the metal like angry bees. He could measure the energy carried by these flying electrons, and they all the same value.

If he shone more intense light at this frequency he certainly got more electrons, but the energy they contained was still the same. More light increased the quantity of electrons ejected, but did not affect the quantity of the energy each electron carried.

Moving to light of higher and higher frequencies (such as violet light), however, did affect the quantity of energy carried by the ejected electrons - it increased! There was a relationship between the frequency of the light used and the amount of energy carried by the escaping electrons.

In 1905 Einstein explained the photoelectric effect using the recent discoveries of Plank and the quanta of energy carried by light photons. What was happening, he said, was that the electrons in the metal were being bombarded by photons carry their quantum packets of energy. Red light had photons with too little energy to dislodge an electron from its atom. But blue or violet light had photons with quanta large enough to knock the metal electrons into outer space. It all depended on the quantity of energy carried by photon.

The size of the quanta of energy was directly related to the frequency of the light. Long wavelength-low frequency light (such as red light) did not have quanta large enough to do the job, whereas shorter wavelength-higher frequency light (such as violet or blue light), had quanta large enough to over come the forces of attraction within the metal atom and send the electron spinning away.

Einstein's explanation of the photoelectric effect is now generally considered to be the start of our understanding of quantum mechanics, or quantum physics. It was a very elegant explanation of a phenomenon that could not be easily understood any other way. This, however, did not make it easy to appreciate.

It did imply something about electrons, however. Just like the photons in light consisted of different quanta of energy depending on their wavelength and frequency, electrons could also contain different quanta of energy depending on ... what?