Radiation Pressure.

21. Radiant energy or radiation consists of electromagnetic waves in the aether. Maxwell's electromagnetic theory showed that these waves possess momentum. If E is the energy of the waves, c the velocity of light, the momentum is E/c in the direction in which the waves are travelling.

According to the modern view energy and mass are inseparable, c2 ergs corresponding to 1 gm. This leads immediately to the same result. For the energy E ergs indicates a mass E/c2 gm., and since the velocity is c the momentum is (E/c2) × c = E/c.

A material screen which absorbs the waves absorbs also their momentum. Thus the momentum of the screen changes, which is another way of saying that it is acted on by a force. Suppose that waves containing E ergs per cu. cm. impinge normally on a perfectly absorbing surface. A column of radiation of height c passes into and is absorbed by each sq. cm. of the surface per sec.; this column contains Ec ergs and the momentum is thus Ec/c or E units. The force on the screen is thus E dynes per sq. cm.

For imperfect absorbers we must deduct the proportion of the momentum which is not passed on to the material screen, viz. that of the transmitted, scattered or reflected waves. For example, a perfect reflector would experience a pressure 2E; half of this is due to its stoppage of the incident waves and half is the recoil due to the projection of the train of reflected waves.

Interaction of Radiation and Matter.

34. The theory of the equilibrium of matter and radiation at constant temperature depends on a principle which is a generalisation of the theory of exchanges (§ 29). After equilibrium is reached no visible change occurs; the density and constitution of the radiation, the proportion of atoms in various states of combination and ionisation, the number of free electrons, the proportion of molecular velocities between given limits, all remain steady; but beneath this statistical changelessness there is continual change happening to the individual atoms, electrons, and elements of radiation.

Consider the atoms of a particular element which are uncombined and in their normal neutral state. The number n of these atoms in the system will remain constant (apart from chance fluctuations) when equilibrium is reached. But the individuals composing this number continually change. New atoms appear in this state owing to the dissolution of chemical molecules containing them, neutralisation of ionised atoms by the capture of free electrons, relapse of excited atoms to the normal state. Atoms in the given state disappear owing to the converse processes—combination to form chemical molecules, ionisation by the expulsion of an electron, excitation by absorption of radiation or collision with electrons or atoms. The steadiness of n is due to an average balancing of gains and losses.

But the principle above mentioned is not content with formulating this general balance of gain and loss—a mere translation of the word “equilibrium.”

Ionisation.

173. The determination of the degree of ionisation of the atoms under the conditions of temperature and density found in the stars is important in connection with the following applications—

(a) We derive from it the molecular weight μ which is required for nearly all numerical calculations. Accuracy is important since μ is often raised to a rather high power in the formulae. We have to find—

(1) What is the most probable value of μ for the stars in general? (The standard value adopted by us is 2·1.)

(2) What is the magnitude of the differential effects (more particularly as affecting the mass-luminosity relation) caused by differences of μ between different stars?

(3) What is the change of μ between the centre and the outer parts of a star?

(b) A knowledge of the ionisation is required in connection with theories of absorption, since each ionisation destroys an absorbing mechanism; in particular, it determines the “guillotine” correction to the opacity on Kramers' theory.

(c) It determines the energy of ionisation of a star and hence the ratio of specific heats γ, which is important in the study of the pulsations of Cepheids.

Another subject appropriately treated in connection with ionisation is the determination of the deviation of stellar material from the laws of a perfect gas.

The results generally depend appreciably on the chemical constitution of a star.