The quantum theory of radiation

The quantum theory of radiation – İngilizce ileri düzey okuma parçası (advanced reading)

Now, before the quantum theory was put forward, there was no notion of natural units of radiant energy: it was believed that we could have any amount of energy, as small as we pleased, radiated by a hot body or a luminous atom. It could, however, be shown mathematically that, if this were true, we should expect a hot body to radiate nearly all its energy in the violet and ultraviolet end of the spectrum, which we know to be against the facts of observation.

The problem was solved in the first year of the present century, when Planck showed that, to get the right result, it was necessary to make a revolutionary hypothesis: to suppose that radiant energy was sent out in packets, as it were – in units or atoms of energy, just as matter existed in atomic units. We cannot have less than an atom of lead, say; any minute piece of lead must consist of a whole number of atoms. We cannot have an electric charge of less than an electron. In the same way, we cannot have less than a unit – or quantum, as it is called – of radiant energy, and any body that sends out or absorbs radiation must deal with one quantum or a whole number of quanta.

The little parcel of light of one particular frequency in which radiant energy is delivered is sometimes called a ‘light dart’, a very expressive term, but is more generally known as a photon. The photon is simply a quantum of radiant energy, the only object of sometimes using the new term being that ‘quantum’ is a more inclusive term, which can be applied to other things as well as light – for instance, to the vibration of whole atoms and molecules.

The quantum of radiant energy differs from the quantum of electricity, the electron, in a very important way. The amount of charge is the same on all electrons: there is but one unit. The magnitude of this unit of radiant energy, however, is different for every different kind-that is, for every different wave-length – of radiation. It is, in fact, proportional to the frequency, so that the quantum of energy of extreme visible red radiation is only half that of the extreme visible violet radiation, which, as we have said before, has double the frequency. The quantum of an X-radiation is very much greater than the quantum of any visible radiation.

The quantum of energy corresponding to a given species of radiation is found, then, by multiplying the frequency by a certain fixed number, which is called Planck’s universal constant, and always indicated by h. Planck’s constant enters into every aspect of modern atomic physics and its numerical value has been found by at least ten different methods, involving such things as X-ray properties, the distribution of energy in black-body radiation, the frequencies of spectral lines, and so on. All the methods give values agreeing to within a few parts in ten thousand.

Light, then, or radiation in general, has a packet property as well as a wave property, and this is one of the paradoxes of modern physics. Newton’s conception of light was a stream of particles, which he endowed with something in the nature of pulsating properties in an attempt to account for certain phenomena which we can now easily explain on the wave theory. He felt the need for the double aspect, the particle and the periodic, and provided for it in his theory.
If white light could be considered to consist of particles of various sizes, corresponding to all the different colours which it contains, it would be fairly easy to imagine the amount of energy in each particle to depend upon its size, and the quantum, or atomic, nature of the energy would be a natural consequence. We could have one or two or three particles of sodium light, but not a fraction of a particle. However, to account for the various phenomena of interference and diffraction, we have to admit that light behaves under some conditions as a stream of particles, each one of which has a fixed energy belonging to it, and under other conditions as a wave motion. Both wave aspects and particle aspects are included today in a comprehensive theory known as wave mechanics.

Thus in geometrical optics we usefully treat light as travelling in straight lines through lenses, although we know that it has wave properties which must be considered when optical resolution is in question. In the simple kinetic theory of gases – say, for working out the action of high-vacuum pumps – we can safely treat atoms as small elastic particles and neglect their structure. The essential is to know which aspect is the dominating one in the problem concerned.

Take, first of all, the photo-electric effect. We have seen that, when light or any radiation of short wave-length falls on a metal, electrons are shot off, the number depending on the strength of the light; but the speed, or more correctly the energy, on the kind of light. If the radiation is done up in packets of energy, and this energy can be expended in pushing out electrons, then clearly we should expect each atom of light either to throw out an electron with a definite speed, or to do nothing; but not to throw out an electron with some greater speed. According to the quantum theory, a short wave-length – that is, a high-frequency – radiation should therefore throw out electrons with an energy of motion greater than that which characterizes electrons ejected by radiation of long wave-length.

This is just what is observed; red light does not eject electrons at all from most metals, violet light drives them out with a small speed, ultra-violet light produces greater speed, and X-rays throw out very fast electrons. Red light, the quanta of which are very small, on account of its low frequency, has no effect, because a certain minimum energy is required just to jerk an electron out of an atom: the energy of the red quanta is, for most metals, less than this minimum. Allowing for the small energy required just to free the electron, the energy which the electron acquires can be shown experimentally to be exactly proportional to the frequency of the radiation. This is now so well established that, in cases where it is difficult to measure the frequency of very short ultra-violet waves by ordinary means, the energy of the electrons which they eject from matter has been determined, and taken as a measure of the wave-length. The same method has been applied to the exceedingly high-frequency gamma rays of radium.

(From An Approach to Modern Physics by E. N. Da C. Andrade.)