A system of physical chemistry - Index of

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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.

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