PART VI.
113. Comparison of the ionization produced by the α and β rays. With unscreened active material the ionization produced between two parallel plates, placed as in [Fig. 17], is mainly due to the α rays. On account of the slight penetrating power of the α rays, the current due to them practically reaches a maximum with a small thickness of radio-active material. The following saturation currents were observed[[181]] for different thicknesses of uranium oxide between parallel plates sufficiently far apart for all the α rays to be absorbed in the gas between them.
Surface of uranium oxide 38 sq. cms.
| Weight of uranium oxide in grammes per sq. cm. of surface | Saturation current in amperes per sq. cm. of surface |
|---|---|
| . | |
| ·0036 | 1·7 × 10-13 |
| ·0096 | 3·2 × 10-13 |
| ·0189 | 4·0 × 10-13 |
| ·0350 | 4·4 × 10-13 |
| ·0955 | 4·7 × 10-13 |
The current reached about half its maximum value for a weight of oxide ·0055 gr. per sq. cm. If the α rays are cut off by a metallic screen, the ionization is then mainly due to the β rays, since the ionization produced by the γ rays is small in comparison. For the β rays from uranium oxide it has been shown ([section 86]) that the current reaches half its maximum value for a thickness of 0·11 gr. per sq. cm.
Meyer and Schweidler[[182]] have found that the radiation from a water solution of uranium nitrate is very nearly proportional to the amount of uranium present in the solution.
On account of the difference in the penetrating power of the α and β rays, the ratio of the ionization currents produced by them depends on the thickness of the radio-active layer under examination. The following comparative values of the current due to the α and β rays were obtained for very thin layers of active matter[[183]]. A weight of ⅒ gramme of fine powder, consisting of uranium oxide, thorium oxide, or radium chloride of activity 2000, was spread as uniformly as possible over an area of 80 sq. cms. The saturation current was observed between parallel plates 5·7 cms. apart. This distance was sufficient to absorb most of the α rays from the active substances. A layer of aluminium ·009 cm. thick absorbed all the α rays.
| Current due to α rays | Current due to β rays | Ratio of currents β/α | |
|---|---|---|---|
| Uranium | 1 | 1 | ·0074 |
| Thorium | 1 | ·27 | ·0020 |
| Radium | 2000 | 1350 | ·0033 |
In the above table the saturation current due to the α and β rays of uranium is, in each case, taken as unity. The third column gives the ratio of the currents observed for equal weights of substance. The results are only approximate in character, for the ionization due to a given weight of substance depends on its fineness of division. In all cases, the current due to the β rays is small compared with that due to the α rays, being greatest for uranium and least for thorium. As the thickness of layer increases, the ratio of currents β/α steadily increases to a constant value.
114. Comparison of the energy radiated by the α and β rays. It has not yet been found possible to measure directly the energy of the α and β rays. A comparison of the energy radiated in the two forms of rays can, however, be made indirectly by two distinct methods.
If it be assumed that the same amount of energy is required to produce an ion by either the α or the β ray, and that the same proportion of the total energy is used up in producing ions, an approximate estimate can be made of the ratio of the energy radiated by the α and β rays by measuring the ratio of the total number of ions produced by them. If λ is the coefficient of absorption of the β rays in air, the rate of production of ions per unit volume at a distance x from the source is
where q₀ is the rate of ionization at the source.
The total number of ions produced by complete absorption of the rays is
Now λ is difficult to measure experimentally for air, but an approximate estimate can be made of its value from the known fact that the absorption of β rays is approximately proportional to the density of any given substance.
For β rays from uranium the value of λ for aluminium is about 14, and λ divided by the density is 5·4. Taking the density of air as ·0012, we find that for air
λ = ·0065.
The total number of ions produced in air is thus 154q₀ when the rays are completely absorbed.
Now from the above table the ionization due to the β rays is ·0074 of that produced by α rays, when the β rays passed through a distance of 5·7 cms. of air.
Thus we have approximately
Total number of ions produced by β rays ·0074
--------------------------------------- = ----- × 154 = 0·20.
Total number of ions produced by α rays 5·7
Therefore about ⅙ of the total energy radiated into air by a thin layer of uranium is carried by the β rays or electrons. The ratio for thorium is about ¹⁄₂₂ and for radium about ¹⁄₁₄, assuming the rays to have about the same average value of λ.
This calculation takes into account only the energy which is radiated out into the surrounding gas; but on account of the ease with which the α rays are absorbed, even with a thin layer, the greater proportion of the radiation is absorbed by the radio-active substance itself. This is seen to be the case when it is recalled that the α radiation of thorium or radium is reduced to half value after passing through a thickness of about 0·0005 cm. of aluminium. Taking into consideration the great density of the radio-active substances, it is probable that most of the radiation which escapes into the air is due to a thin skin of the powder not much more than ·0001 cm. in thickness.
An estimate, however, of the relative rate of emission of energy by the α and β rays from a thick layer of material can be made in the following way:—For simplicity suppose a thick layer of radio-active substance spread uniformly over a large plane area. There seems to be no doubt that the radiations are emitted uniformly from each portion of the mass; consequently, the radiation, which produces the ionizing action in the gas above the radio-active layer, is the sum total of all the radiation which reaches the surface of the layer.
Let λ1 be the average coefficient of absorption of the α rays in the radio-active substance itself and σ the specific gravity of the substance. Let E1 be the total energy radiated per sec. per unit mass of the substance when the absorption of the rays in the substance itself is disregarded. The energy per sec. radiated to the upper surface by a thickness dx of a layer of unit area at a distance x from the surface is given by
The total energy W1 per unit area radiated to the surface per sec. by a thickness d is given by
if λ1d is large.
In a similar way it may be shown that the energy W2 of the β rays reaching the surface is given by
where E2 and λ2 are the values for the β rays corresponding to E1 and λ1 for the α rays. Thus it follows that
E1 λ1W1
---- = ------
E2 λ2W2
λ1 and λ2 are difficult to determine directly for the radio-active substance itself, but it is probable that the ratio λ1/λ2 is not very different from the ratio for the absorption coefficients for another substance like aluminium. This follows from the general result that the absorption of both α and β rays is proportional to the density of the substance; for it has already been shown in the case of the β rays from uranium that the absorption of the rays in the radio-active material is about the same as for non-radio-active matter of the same density.
With a thick layer of uranium oxide spread over an area of 22 sq. cms., it was found that the saturation current between parallel plates 6·1 cms. apart, due to the α rays, was 12·7 times as great as the current due to the β rays. Since the α rays were entirely absorbed between the plates and the total ionization produced by the β rays is 154 times the value at the surface of the plates,
W1 total number of ions due to α rays
---- = ------------------------------------
W2 total number of ions due to β rays
12·7 × 6·1
= ------------- = 0·5 approximately.
154
Now the value of λ1 for aluminium is 2740 and of λ2 for the same metal 14, thus
E1 λ1W1
---- = ------- = 100 approximately
E2 λ2W2
This shows that the energy radiated from a thick layer of material by the β rays is only about 1 per cent. of the energy radiated in the form of α rays.
This estimate is confirmed by calculations based on independent data. Let m1, m2 be the masses of the α and β particles respectively and v1, v2 their velocities.
Now it has been shown that for the α rays of radium
v1 = 2·5 × 109,
e
--- = 6 × 103.
m1
The velocity of the β rays of radium varies between wide limits. Taking for an average value
v2 = 1·5 × 1010,
e
---- = 1·8 × 107,
m1
it follows that the energy of the α particle from radium is almost 83 times the energy of the β particle. If equal numbers of α and β particles are projected per second, the total energy radiated in the form of α rays is about 83 times the amount in the form of β rays.
Evidence will be given later ([section 253]) to show that the number of α particles projected is probably four times the number of β particles; so that a still greater proportion of the energy is emitted in the form of α rays. These results thus lead to the conclusion that, from the point of view of the energy emitted, the α rays are far more important than the β rays. This conclusion is supported by other evidence which is discussed in chapters [XII] and [XIII], where it will be shown that the α rays play by far the most important part in the changes occurring in radio-active bodies, and that the β rays only appear in the latter stages of the radio-active processes. From data based on the relative absorption and ionization of the β and γ rays in air, it can be shown that the γ rays carry off about the same amount of energy as the β rays. These conclusions are confirmed by direct measurement of the heating effect of radium, which is discussed in detail in [chapter XII].
CHAPTER V.
PROPERTIES OF THE RADIATIONS.
115. Besides their power of acting on a photographic plate, and of ionizing gases, the radiations from active bodies are able to produce marked chemical and physical actions in various substances. Most of these effects are due either to the α or β rays. The γ rays produce little effect in comparison. Since the β rays are similar in all respects to high velocity cathode rays, it is to be expected that they will produce effects similar in character to those produced by the cathode rays in a vacuum tube.