Page:Radio-activity.djvu/78

 occasionally produced by collision when the negative ion moves freely between two points differing in potential by 10 volts. If the difference be about V = 20 volts, fresh ions arise at each collision.

Now the energy W, acquired by an ion of charge e moving freely between two points at a difference of potential V, is given by

$$W = Ve$$.

Taking V = 20 volts = 20/300 units, and e = 3·4 × 10^{-10}, the energy W required in the case of a negative ion to produce an ion by collision is given by

W = 2·3 × 10^{-11} ergs.

The velocity u acquired by the ion of mass m just before a collision is given by

$$\frac{1}{2}mu^2 = Ve$$,

and     $$u = \sqrt{\frac{2Ve}{m}}$$.

Now e/m = 1·86 × 10^7 electromagnetic units for the electron at slow speeds (section 82).

Taking V = 20 volts, we find that

u = 2·7 × 10^8 cms. per sec.

This velocity is very great compared with the velocity of agitation of the molecules of the gas.

In a weak electric field, the negative ions only produce ions by collision. The positive ion, whose mass is at least 1000 times greater than the electron, does not acquire a sufficient velocity to generate ions by collision until an electric field is applied nearly sufficient to cause a spark through the gas.

An estimate of the energy required for the production of an ion by X rays has been made by Rutherford and M^cClung. The energy of the rays was measured by their heating effect, and the total number of ions produced determined. On the assumption that all the energy of the rays is used up in producing ions, it