A system of physical chemistry - Index of

126 A SYSTEM OF PHYSICAL CHEMISTRY

It seems more reasonable to suppose that the velocity is imparted by

the light, and yet, as we have seen, the velocity is independent **of**

the intensity **of** the light. These results can, however, be reconciled

by the view stated above, that a wave **of** is

light not a continuous

structure, but that its energy is concentrated in units (the places where

the lines **of** force are disturbed), and that the energy in each **of** these

units does not diminish as it travels its along line **of** force. Thus if a

unit by impinging on a molecule can at any place make it liberate a

corpuscle, it will do so and start the corpuscle with the same velocity

whatever may be the distance from the source when it strikes the

molecule thus the ; velocity **of** the corpuscles would be independent

**of** the intensity **of** the light. Ladenburg found that the velocity **of** the

corpuscle increases with the frequency **of** the light ; this shows that, if

the view we are discussing is correct, the energy in the units will increase

with the frequency **of** the light. This latter statement is, **of**

course, in complete agreement with the quantum hypothesis, according

to which the energy in any unit is directly proportional to the frequency,

i.e. t = hv.

Einstein has given a quantitative application

**of** the quantum

hypothesis to the photo-electric effect in the expression —

V^ = \mTp- = hv — kvQ.

The term ^mv^ is the kinetic energy **of** the electron emitted by light **of**

frequency v. vo is the threshold frequency already defined, characteristic

**of** the substance from which the electrons are emitted. The significance

**of** Ye has already been pointed out. It follows from the above

expression that when v = vq the electron will just not be emitted, vq

being therefore the lower limit **of** frequency capable **of** bringing about

the photo-electric effect at all. Further, the frequency is proportional

to the kinetic energy and therefore to the square **of** the velocity **of** the

electron.

The applicability **of** the quantum theory to the photo-electric effect

may be regarded as evidence **of** considerable value in favour **of** the

quantum hypothesis itself— especially in the form given to it by

Einstein.

Sir J. J. Thomson has Hkewise made an attempt to calculate the

amount **of** energy in each unit **of** light **of** given frequency from some **of**

Lenard's data. With the ultra-violet light used by Lenard the maximum

velocity **of** the corpuscles was about lo^ cms. per second the

;

kinetic energy {^mv-) **of** a corpuscle moving with this is speed about

3 X iQ-^"^ ergs.

If we suppose that the energy **of** the corpuscle liberated

is **of** the same magnitude as that **of** the light unit € which liberated

the corpuscle, we would e expect (for the given light) to be about lo-^"-

ergs. It will be seen that this agrees very well with the values for c

already given as a result **of** calculation, with the help **of** Planck's constant

h. A similar calculation, with equally satisfactory results, has been

recently carried out by J. Franck and G. Hertz {Verh. d. d. physik.