A system of physical chemistry - Index of

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A system of physical chemistry - Index of

APPENDIX II 179

and that at any instant the energy of an oscillator can only be an

integral multiple of a finite unit or "quantum " of energy, the amount

of the unit depending on the frequency. It is to be carefully noted

that this does not imply, of necessity, an atomic structure for —

energy

a view, indeed, repudiated by Planck it ; does imply that the oscillator

must emit or absorb whole quanta of radiation at one time (at present,

be it noted, we are discussing Planck's earlier views). Now such an

assumption necessarily involves a modification of Maxwell's distribution

law, for that law depends on the possibility of the infinite divisability

of the energy among the oscillators, atoms, molecules, and so forth.

The point is more easily followed with aid of a "condition-diagram".

Suppose we denote the charges of the doublets as ±^, the mass of the

vibrating particle as w, and x as its displacement along its axis at time /,

then the equation of its " free " motion is—

X + 47r"^i'^ . X

or 7nx + 47r"i'-' . mx

— O

= o

where v is the frequency. If X is the resolved component of the

electric intensity of the field along x at time /, the equation of its

forced motion is—

mx + ^TT^vhnx =^X .

If we denote the energy of the particle by c—

• O , 9 9 '>

mx'' + ^ir'v''mx- = 2£,

or denoting its momentum h-^ y{ = — mx)

. . •

y"f-

ATT'v^in . x'^ = 2e . . . . f"?) ^ '

m

Now the condition of any oscillator as regards the displacement and

momentum of its vibrating particle can be clearly represented on a plane

diagram by a point with co-ordinates x and y. All those oscillators

whose energy is c have their representative points lying on the ellipse—

A-2

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