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 Saturation current oxide in grammes per in amperes per sq. sq. cm. of surface 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 Current Ratio of due to α due to β currents rays rays 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

$$ q₀ e^{–λ x} $$

where _q₀_ is the rate of ionization at the source.

The total number of ions produced by complete absorption of the rays is

$$ \int₀^{\infty} q₀ e^{–λ x} dx = \frac {q₀} {λ} $$,

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 154_q₀_ 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

$$ \frac {1} {2} E_1 \sigma e^{–λ_1 x} dx $$ .

The total energy _W₁_ per unit area radiated to the surface per sec. by a thickness _d_ is given by

$$ W_1 = \frac {1}{2} \int₀^d E_1 \sigma e^{–λ_1 x} dx $$ $$ = \frac {E_1 \sigma} {2 λ_1} (1 − e^{–λ_1 d}) $$ $$ = \frac {E_1 \sigma} {2 λ_1} $$

if λ₁_d_ is large.

* * * * *

In a similar way it may be shown that the energy _W₂_ of the β rays reaching the surface is given by

$$ W_2 = \frac {E_2 \sigma} {2 λ_2} $$

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_ λ₁_W₁_ ---- = ------ _E₂_ λ₂_W₂_

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_ λ₁_W₁_ ----- = ---------- = 100 approximately _E₂_ λ₂_W₂_

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.

$$ \frac {Energy of one \alpha particle} {Energy of one \beta particle} = \frac {m_1 v_1^2} {m_2 v_2^2} $$ $$ = \frac {\frac {m_1} {e} v_1^2} {\frac {m^2} {e} v_2^2} $$ .

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, _m₂_

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.

Footnote 111:

In an examination of uranium the writer (_Phil. Mag._ p. 116, Jan. 1899) found that the rays from uranium consist of two kinds, differing greatly in penetrating power, which were called the α and β rays. Later, it was found that similar types of rays were emitted by thorium and radium. On the discovery that very penetrating rays were given out by uranium and thorium as well as by radium, the term γ was applied to them by the writer. The word “ray” has been retained in this work, although it is now settled that the α and β rays consist of particles projected with great velocity. The term is thus used in the same sense as by Newton, who applied it in the _Principia_ to the stream of corpuscles which he believed to be responsible for the phenomenon of light. In some recent papers, the α and β rays have been called the α and β “emanations.” This nomenclature cannot fail to lead to confusion, since the term “radio-active emanation” has already been generally adopted in radio-activity as applying to the material substance which gradually _diffuses_ from thorium and radium compounds, and itself emits rays.

Footnote 112:

This method of illustration is due to Mme Curie, _Thèse présentée à la Faculté des Sciences de Paris_, 1903.

Footnote 113:

Giesel, _Annal. d. Phys._ 69, p. 834, 1899.

Footnote 114:

Meyer and Schweidler, _Phys. Zeit._ 1, pp. 90, 113, 1899.

Footnote 115:

Becquerel, _C. R._ 129, pp. 997, 1205, 1899.

Footnote 116:

Curie, _C. R._ 130, p. 73, 1900.

Footnote 117:

Rutherford, _Phil. Mag._ January, 1899.

Footnote 118:

Rutherford and Grier, _Phil. Mag._ September, 1902.

Footnote 119:

Becquerel, _C. R._ 130, pp. 206, 372, 810, 979. 1900.

Footnote 120:

M. and Mme Curie, _C. R._ 130, p. 647, 1900.

Footnote 121:

The activity of the radium preparation was not stated in the paper.

Footnote 122:

Dorn, _Phys. Zeit._ 4, No. 18, p. 507, 1903.

Footnote 123:

Strutt, _Phil. Mag._ Nov. 1903.

Footnote 124:

Wien, _Phys. Zeit._ 4, No. 23, p. 624, 1903.

Footnote 125:

Dorn, _C. R._ 130, p. 1129, 1900.

Footnote 126:

Becquerel, _C. R._ 130, p. 809, 1900.

Footnote 127:

Kaufmann, _Phys. Zeit._ 4, No. 1 b, p. 54, 1902.

Footnote 128:

Abraham, _Phys. Zeit._ 4, No. 1 b, p. 57, 1902.

Footnote 129:

Kaufmann, _Nachrichten d. Ges. d. Wiss. zu Gött._, Nov. 8, 1901.

Footnote 130:

Simon, _Annal. d. Phys._ p. 589, 1899.

Footnote 131:

Kaufmann, _Phys. Zeit._ 4, No. 1 b, p. 54, 1902.

Footnote 132:

Paschen, _Annal. d. Phys._ 14, p. 389, 1904.

Footnote 133:

Meyer and Schweidler, _Phys. Zeit._ pp. 90, 113, 209, 1900.

Footnote 134:

Lenard, _Annal. d. Phys._ 56, p. 275, 1895.

Footnote 135:

Strutt, _Nature_, p. 539, 1900.

Footnote 136:

Seitz, _Phys. Zeit._ 5, No. 14, p. 395, 1904.

Footnote 137:

It is presumed that the results were corrected, if necessary, for the discharging action due to the ionized gas, although no direct mention of this is made in the paper by Seitz.

Footnote 138:

Strutt, _Phil. Trans._ A, p. 507, 1901.

Footnote 139:

Crookes, _Proc. Roy. Soc._ 1902. _Chem. News_, 85, p. 109, 1902.

Footnote 140:

Mme Curie, _C. R._ 130, p. 76, 1900.

Footnote 141:

Rutherford, _Phil. Mag._ Feb. 1903. _Phys. Zeit._ 4, p. 235, 1902.

Footnote 142:

Becquerel, _C. R._ 136, p. 199, 1903.

Footnote 143:

Becquerel, _C. R._ 136, p. 431, 1903.

Footnote 144:

Des Coudres, _Phys. Zeit._ 4, No. 17, p. 483, 1903.

Footnote 145:

Becquerel, _C. R._ 136, p. 1517, 1903.

Footnote 146:

Bragg, _Phil. Mag._ Dec. 1904; Bragg and Kleeman, _Phil. Mag._ Dec. 1904.

Footnote 147:

Further experimental results bearing on this important question are given in an Appendix to this book.

Footnote 148:

Bakerian Lecture, _Phil. Trans._ A, p. 169, 1904.

Footnote 149:

Strutt, _Phil. Mag._ Aug. 1904.

Footnote 150:

J. J. Thomson, _Proc. Camb. Phil._ Soc. 13, Pt. I. p. 39, 1905. _Nature_, Dec. 15, 1904.

Footnote 151:

Rutherford, _Nature_, March 2, 1905. J. J. Thomson, _Nature_, March 9, 1905.

Footnote 152:

Crookes, _Proc. Roy. Soc._ 81, p. 405, 1903.

Footnote 153:

Elster and Geitel, _Phys. Zeit._ No. 15, p. 437, 1903.

Footnote 154:

Glew, _Arch. Röntgen Ray_, June 1904.

Footnote 155:

Becquerel, _C. R._ 137, Oct. 27, 1903.

Footnote 156:

Tommasina, _C. R._ 137, Nov. 9, 1903.

Footnote 157:

An interesting side-light is thrown on this question by the experiments described in Appendix A of this book.

Footnote 158:

Rutherford and Miss Brooks, _Phil. Mag._ July 1902.

Footnote 159:

In order to obtain a thin layer, the compound to be tested is ground to a fine powder and then sifted through a fine gauge uniformly over the area, so that the plate is only partially covered.

Footnote 160:

Rutherford, _Phil. Mag._ Jan. 1899.

Footnote 161:

Owens, _Phil. Mag._ Oct. 1899.

Footnote 162:

Rutherford and Miss Brooks, _Phil. Mag._ July, 1900.

Footnote 163:

Since the ionization at any point above the plate is the resultant effect of the α particles coming from all points of the large radio-active layer, λ is not the same as the coefficient of absorption of the rays from a point source. It will however be proportional to it. For this reason λ is called the “absorption constant.”

Footnote 164:

Townsend, _Phil. Mag._ Feb. 1901.

Footnote 165:

Durack, _Phil. Mag._ July 1902, May 1903.

Footnote 166:

Bragg and Bragg and Kleeman, _Phil. Mag._ Dec. 1904.

Footnote 167:

Villard, _C. R._ 130, pp. 1010, 1178, 1900.

Footnote 168:

Becquerel, _C. R._ 130, p. 1154, 1900.

Footnote 169:

Rutherford, _Phys. Zeit._ 3, p. 517, 1902.

Footnote 170:

McClelland, _Phil. Mag._ July 1904.

Footnote 171:

Paschen, _Phys. Zeit._ 5, No. 18, p. 563, 1904.

Footnote 172:

A. S. Eve, _Phil. Mag._ Nov. 1904.

Footnote 173:

Paschen, _Annal. d. Physik_, 14, p. 114, 1904; 14, 2, p. 389, 1904. _Phys. Zeit._ 5, No. 18, p. 563, 1904.

Footnote 174:

Paschen, _Phys. Zeit._ 5, No. 18, p. 563, 1904.

Footnote 175:

Rutherford and Barnes, _Phil. Mag._ May 1905. _Nature_, p. 151, Dec. 15, 1904.

Footnote 176:

Barkla, _Nature_, March 17, 1904.

Footnote 177:

Becquerel, _C.R._ 132, pp. 371, 734, 1286. 1901.

Footnote 178:

Mme Curie, _Thèse présentée à la Faculté des Sciences_, Paris 1903, p. 85.

Footnote 179:

A. S. Eve, _Phil. Mag._ Dec. 1904.

Footnote 180:

In a recent paper (_Phil. Mag._ Feb. 1905), McClelland has, in the main, confirmed the experimental results obtained by Eve. An electrometer was used instead of an electroscope. He finds, in addition, that the amount of secondary radiation depends on the angle of incidence of the primary rays, and is greatest for an angle of 45°. In a letter to _Nature_ (Feb. 23, p. 390, 1905), he states that more recent experiments have shown that the amount of secondary radiation from different substances is a function of their atomic weights rather than of their densities. In every case examined, the amount of secondary radiation increases with the atomic weight, but is not proportional to it.

Footnote 181:

Rutherford and McClung, _Phil. Trans._ A. p. 25, 1901.

Footnote 182:

Meyer and Schweidler, _Wien Ber._ 113, July, 1904.

Footnote 183:

Rutherford and Grier, _Phil. Mag._ Sept. 1902.