DISCOVERY 



225 



with a \'ie\v to discovering the relations between the 

 wave length of the ether radiations and the velocity 

 of the ejected electrons. But the experimental diffi- 

 culties of obtaining a close insight into the effect were 

 always considerable until we had to do with the new 

 variety of light which Rontgen discovered in 1895. 

 The very short wave length which is associated with 

 X-rays goes \\-ith a photo-electric effect which is so 

 greatly intensified that we can examine it in detail, 

 and now the relation between wave and electron takes 

 on an importance which arrests attention. 



We can take the question in two stages : in the first 

 as a general question. In the second we bring in 

 effects which depend on details of atomic structure. 



The general question can be stated quite simply. 

 We have seen that a wave motion is defined by two 

 qualities. The one the wave length ; the other the 

 amplitude. WTtien an X-ray falls upon any material 

 substance we find that electrons are ejected ; the wave 

 radiation has produced an electron radiation. Elec- 

 tron radiation has characteristics also, namely, number 

 and speed. In what way, then, are the characteristics 

 of the waves related to the characteristics of the 

 electron movements which are e.xcited by them ? The 

 answer is simple but surely unexpected. The velocity 

 of the electron depends on the wave length only ; the 

 number of electrons depends on the intensity, but not 

 on the wave length. Moreover, the relation between 

 the wave length of the one radiation and the velocity 

 of the other is of the simplest kind. If we define the 

 wave length by stating the number of waves that pass 

 by a given point in a second and call this number the 

 frequency, then the energy of the electron is equal to 

 the frequency multiplied by a constant quantity. This 

 constant is not new to us, it had already turned up in 

 connection with investigation of interchange of energy, 

 where waves are concerned, and is w'ell known as 

 Planck's constant. That, however, need not concern 

 us now. 



The essential point is that a wave radiation falling on 

 matter of any kind whatever and in any physical condi- 

 tion, liquid or solid or gaseous, hot or cold, causes the 

 ejection of electrons. In actual experiment we cannot 

 usually examine the speed of the electron at the instant 

 of its production. We have generally to wait for the 

 electrons to get outside the body in which they arise 

 before we can handle them in our experiments. Those 

 that have come through the deeps of the material have 

 lost speed by collision with the atoms on their way out. 

 Consequently, we have in response to the incidence of 

 waves of a definite frequency, that is to say, of so-called 

 monochromatic radiation, an output of electrons of 

 various speeds ranging downwards from a maximum 

 which is given by the above-mentioned relation. There 

 does not seem to be any doubt that the electrons all had 



originally quite the same definite speed, and that the 

 differences in speed are acquired subsequently. 



In this process we see energy of wave radiation 

 replaced by energy of electron radiation. There is an 

 exactly converse process. If we direct a stream of 

 electrons against any material substance we can call into 

 being ether waves. They arise at the point of impact, 

 and their quality is, in the general sense, determined 

 by the velocity which we have given the electron 

 stream. 



Among the waves so originated there are some whose 

 frequency is related to the energy of the individual 

 electron in the electron stream by the same constant 

 as before. There are others of lesser frequency, such 

 as we might suppose to be originated by electrons that 

 belonged to the original stream, but have lost energy 

 by collisions with the atoms of matter. Here, again, 

 there is no doubt that the electrons produce waves for 

 which the frequency is exactly determined by the use 

 of Planck's constant as above. 



In order to realise the full significance of these extra- 

 ordinary results, let us picture the double process as it 

 occurs whenever we use an X-ray bulb. By the im- 

 position of great electrical forces we hurl electrons in 

 a stream across the bulb. One of these electrons, let 

 us say, starts a wave where it falls. This action is quite 

 unaffected by the presence of similar actions in the 

 neighbourhood, so that we can fix our minds upon this 

 one electron and the wave which it £done causes to 

 arise. The wave spreads away, it passes through the 

 walls of the bulb, through the air outside, and somewhere 

 or other in its path, in one of the many atoms it passes 

 over, an electron springs into existence, having the 

 same speed as the original in the X-ray bulb. The 

 equality of the two speeds is not necessary to the 

 significance of this extraordinary effect ; it would have 

 been just as wonderful if one speed had only been one- 

 half or one-quarter or any reasonable fraction of the 

 other. The equality is more an indication to us of how 

 to look for an explanation than an additional difficulty 

 to be overcome. 



Let me take an analogy. I drop a log of wood into 

 the sea from a height, let us say, of 100 feet. A wave 

 radiates away from where it falls. Here is the corpus- 

 cular radiation producing a wave. The wave spreads, 

 its energy is more and more widely distributed, the 

 ripples get less and less in height. At a short dis- 

 tance away, a few hundred yards perhaps, the effect will 

 apparently have disappeared. If the water were 

 perfectly free from viscosity and there were no other 

 causes to fritter away the energy of the waves, they 

 would travel, let us say, 1,000 miles. By which time 

 the height of the ripples would be, as we can readily 

 imagine, extremely small. Then, at some one point 

 on its circumference, the ripple encounters a wooden 



