IONIZATION AND BIOLOGICAL EFFECTS 97 



this theory a source of radiation emits "particles" of energy, known as 

 photons, which in a vacuum travel in straight lines with the velocity of 

 light. The factor which, on the undulatory theory, is called wave-length, 

 is represented in this case by the amount of energy in the photon. The 

 shorter the wave-length, the larger is the amount of energy in the photon. 

 Monochromatic radiation consists of photons all of which carry exactly 

 the same amount of energy. A very small source — "point source" — of 

 monochromatic radiation emits, let us say, N photons per second. 

 Since the emission takes place at random, during a certain time the 

 photons are projected uniformly in all directions. If the source is at the 

 center of a sphere, all the photons pierce the surface of this sphere, and 

 furthermore, in a given time the same number pass through equal areas 

 of the surface. The area of a sphere of radius a; cm. is 4x0;^ cm. ^. There- 

 fore the number of photons traversing each square centimeter per second 

 is N/4tx^. If each photon carries an amount of energy hv (cf. Darrow, 

 page 3), the energy passing through each square centimeter per second 

 is Nhv/^TTX^. This is the intensity of radiation at the distance x from the 

 point source in question. If the radiation is polychromatic, it can be 

 divided into its monochromatic components and the intensity of radiation 

 at a given point will then be the sum of the intensities of the individual 

 components. The mathematical relation for the intensity of radiation 



Nhv 



I = 



Airx^ 



can be written in the form 



Nhv 1 



47r x^ 



or, since for a given source and in a vacuum, Nhv /Air is constant, 



K 



I = 



^2 



This is the well-known inverse square law, which states that in a vacuum 

 the intensity of radiation at any distance from a point source is inversely 

 proportional to the square of the distance. 



In most X-ray tubes employed in practice, the radiation is emitted 

 from a small area, the "focal spot" of the target. The distance at which 

 the material to be irradiated is placed is relatively long, and therefore 

 the intensity of radiation follows the inverse square law very closely, 

 in vacuo. The discrepancy introduced by the presence of air can be 

 neglected unless the radiation is very soft." But when radium is used 



^ Certain complications which cannot be discussed here arise in the case of gamma 

 rays, on account of the long range of the secondary beta particles. 



