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Abstracts
MASSES OF LIGHT ELEMENTS DETERMINED FROM NUCLEAR REACTIONS
At the present time the calculation of nuclear reactions is carried out with a sufficient degree of accuracy to make it possible to apply them to the computation of the masses of the elements participating in the reactions. In such calculations it is assumed that the laws of conservation of mass-energy and momentum are valid, against the applicability of which there are no definite proofs.
Investigating the disintegration of lithium by protons and deuterons, Oliphant, Kempton, and Rutherford¹ established that in this case, if one uses mass-spectrographic data for the masses of light elements, agreement with the conservation laws is obtained; i.e., the masses of the particles participating in the reactions, calculated from these reactions, coincide with those obtained mass-spectrographically. However, in the case of nuclear reactions on beryllium it turned out that the masses of light elements calculated from these reactions differ substantially from the masses of the same elements known from mass-spectrographic measurements. This circumstance forced a reconsideration, in some way, of the question of the masses of light elements. In their latest work Oliphant, Kempton, and Rutherford² investigated in detail the nuclear reactions occurring when beryllium is irradiated by protons and deuterons, and also boron by protons.
According to mass-spectrographic data, beryllium consists of a single isotope, whose mass, according to Bainbridge’s measurements, is equal to 9.0155. Studying, with the aid of an ionization chamber connected to a linear amplifier, the radiation emitted when beryllium is irradiated by protons, Rutherford and others² showed that this radiation consists of particles of two kinds. Some particles carry a double charge, others a single charge; at the same time both are present in approximately equal amounts and have the same range, about 7.4 mm of air under normal conditions. It was thereby established that in the nuclear reactions under consideration no γ-radiation is emitted.
To investigate the nature of the particles, their deflection in electric and magnetic fields was carried out. These experiments showed, however, that both kinds of particles are deflected by the fields in the same way and therefore cannot be separated (from the deflection of the particles it was possible to establish that they carry a positive charge). The character of the curve representing the dependence of the deflection of the particles on the magnitude of the field is approximately the same as in the case of polonium α-particles. On this basis it may be thought that the particles with double positive charge are α-particles. Comparing the deflection of the particles under study with the deflection of polonium α-particles in the same electric field, the authors calculated the energy of singly charged and doubly charged particles from the known energy of polonium radiation. For particles with one charge they obtained an energy equal to \(0.55 \cdot 10^6\) eV, and for particles with two charges—\(1.1 \cdot 10^6\) eV. By application of a magnetic field alone it was established that the observed deflection corresponds to the following velocities:
a) for the proton — \(1.40 \cdot 10^9\) cm/sec
b) for the deuteron — \(0.70 \cdot 10^9\) cm/sec
c) for the α-particle — \(0.70 \cdot 10^9\) cm/sec
By comparing the measurements obtained with an electric and a magnetic field, the authors found for the velocity an average value of \(0.73\cdot 10^{9}\ \mathrm{cm/sec}\). Therefore it may be considered established that a particle with a single charge is \({}^{2}\mathrm{H}\), and a particle with a double charge is, in all probability, \({}^{4}\mathrm{He}\). This is further confirmed by the circumstance that the velocity calculated from the range (7.4 mm) is, for \({}^{2}\mathrm{H}\), \(0.77\cdot 10^{9}\ \mathrm{cm/sec}\), and for \({}^{4}\mathrm{He}\), \(0.80\cdot 10^{9}\ \mathrm{cm/sec}\), which agrees quite well with the values given above. The totality of all these data leads the authors to establish the following reactions:
\[ {}^{9}_{4}\mathrm{Be}+{}^{1}_{1}\mathrm{H}\to{}^{8}_{4}\mathrm{Be}+{}^{2}_{1}\mathrm{H}+\beta, \]
\[ {}^{9}_{4}\mathrm{Be}+{}^{1}_{1}\mathrm{H}\to{}^{6}_{3}\mathrm{Li}+{}^{4}_{2}\mathrm{He}+\alpha, \]
where \(\alpha\) and \(\beta\) are the energies liberated in these reactions. Let us note here that \({}^{8}_{4}\mathrm{Be}\) has not hitherto been encountered in nature. If mass-spectrographic data are substituted into the second equation, then for the range of the \(\alpha\)-particles a value of 2.4 cm is obtained, whereas in the result under consideration a value of 7.4 mm is found experimentally. A disagreement with the mass-spectrographic data is also obtained in the case of the reaction occurring with boron when it is bombarded by protons. Studying the absorption of the disintegration products, Oliphant and Rutherford showed in one of their more recent papers that in this case the reaction proceeds according to the following formula:
\[ {}^{11}_{5}\mathrm{B}+{}^{1}_{1}\mathrm{H}\to 3\,{}^{4}_{2}\mathrm{He}+\Theta, \]
while the energy \(\Theta\), liberated in the reaction and measured from the energy of the \(\alpha\)-particles (there is no \(\gamma\)-radiation in any appreciable amount), is about \(9\cdot 10^{6}\ \mathrm{eV}\) [the latest data of the same authors give \((8.5\pm0.6)\cdot 10^{6}\ \mathrm{eV}\)], whereas from the known mass-spectrographic data for B, H, and He one obtains for \(\Theta\) the value \(11.4\cdot 10^{6}\ \mathrm{eV}\). Such a large discrepancy lies far beyond the limits of possible errors.
There also exists a whole series of facts,³ such as, for example, the instability of the \({}^{9}\mathrm{Be}\) nucleus, which indicate that in the values of the masses determined mass-spectrographically there is some error. To clarify the question of a possible error, one must pay attention to the circumstance that, in the case of the disintegration of lithium by protons, the energy liberated in the reaction, calculated from mass-spectrographic data, agrees well with the experimental data obtained in the study of these reactions. It is necessary to note here that the masses of \({}^{1}_{1}\mathrm{H}\), \({}^{2}_{1}\mathrm{H}\), \({}^{6}_{3}\mathrm{Li}\), and \({}^{7}_{3}\mathrm{Li}\) participating in these reactions are all determined, directly or indirectly, with respect to \({}^{4}_{2}\mathrm{He}\), whereas the masses of \({}^{9}_{4}\mathrm{Be}\), \({}^{10}_{5}\mathrm{Be}\), and \({}^{11}_{5}\mathrm{B}\), participating in the reactions in which a contradiction with the mass-spectrographic data is observed, are determined directly or through \({}^{12}_{6}\mathrm{C}\) relative to \({}^{16}_{8}\mathrm{O}\). This comparison leads to the conclusion that the sought error must lie in the ratio \({}^{4}\mathrm{He}:{}^{16}\mathrm{O}\). A unit of mass determined from this not quite exact ratio would give, for other elements, a total error by which, possibly, the discrepancies between the mass-spectrographic data and the data obtained from nuclear reactions are explained. Oliphant, Kempton, and Rutherford² admit the existence of this error without making any assumptions as to the causes from which it arises. They suppose this error, for \({}^{4}\mathrm{He}\) determined with respect to \({}^{16}\mathrm{O}\), to be equal to \(4x\). Then for all elements, in accordance with the method of determining their masses, one can establish the magnitude of the error in mass units \(x\). In the following table the results are given for all elements up to and including \({}^{12}\mathrm{C}\).
To determine the numerical value of \(x\), Rutherford and others used the well-known nuclear reaction
\[ {}^{9}_{4}\mathrm{Be}+{}^{1}_{1}\mathrm{H}\to{}^{6}_{3}\mathrm{Li}+{}^{4}_{2}\mathrm{He}+\alpha. \]
The energy \(\alpha\), liberated in this reaction, is known from experimental data; therefore from this equation one can calculate \(x\), if the masses with corrections borrowed from the third column of Table 1 are introduced into it.
TABLE 1
| Element | Mass determined by mass spectrography | Estimated error | Corrected mass according to Rutherford and others | Corrected mass according to Bethe | Corrected mass according to Aston |
|---|---|---|---|---|---|
| $^{1}_{0}n$ | 1,0080 | $+x$ | $1,0083 \pm 0,0003$ | $1,0085 \pm 0,0005$ | |
| $^{1}_{1}\mathrm{H}$ | 1,0078 | $+x$ | $1,0081 \pm 0,0001$ | $1,00807 \pm 0,00007$ | 1,0081 |
| $^{2}_{1}\mathrm{H}$ | 2,0136 | $+2x$ | $2,0142 \pm 0,0002$ | $2,01423 \pm 0,00015$ | 2,0148 |
| $^{3}_{1}\mathrm{H}$ | — | — | $3,0161 \pm 0,0003$ | $3,01610 \pm 0,00033$ | |
| $^{3}_{2}\mathrm{He}$ | — | — | $3,0172 \pm 0,0003$ | $3,01699 \pm 0,00046$ | |
| $^{4}_{2}\mathrm{He}$ | 4,0022 | $+4x$ | $4,0034 \pm 0,0004$ | $4,00336 \pm 0,00023$ | 4,0041 |
| $^{6}_{3}\mathrm{Li}$ | 6,0145 | $+6x$ | $6,0163 \pm 0,0006$ | $6,01614 \pm 0,00050$ | |
| $^{7}_{3}\mathrm{Li}$ | 7,0146 | $+7x$ | $7,0170 \pm 0,0007$ | $7,01694 \pm 0,00048$ | |
| $^{9}_{4}\mathrm{Be}$ | 9,0155 | $-5x$ | $9,0138 \pm 0,0005$ | $9,0135 \pm 0,0007$ | |
| $^{10}_{5}\mathrm{B}$ | 10,0135 | $+2,5x$ | $10,0143 \pm 0,0003$ | $10,0146 \pm 0,0010$ | |
| $^{11}_{5}\mathrm{B}$ | 11,0110 | ? | 11,0110 | $11,0111 \pm 0,0011$ | |
| $^{12}_{6}\mathrm{C}$ | 12,0036 | $-3x$ | $12,0027 \pm 0,0003$ | $12,0037 \pm 0,0006$ | 12,0048 |
TABLE 2
| Reaction | Energy according to experimental data | Energy calculated from mass-spectrographic data | Energy calculated from corrected masses |
|---|---|---|---|
| $^{6}\mathrm{Li}+{}^{1}\mathrm{H}\to{}^{4}\mathrm{He}+{}^{3}\mathrm{He}$ | $0,0038_{5}$ | 0,0038 | 0,0039 |
| $^{6}\mathrm{Li}+{}^{2}\mathrm{H}\to2\,{}^{4}\mathrm{He}$ | $0,0236_{0}$ | 0,0238 | 0,0236 |
| $^{6}\mathrm{Li}+{}^{2}\mathrm{H}\to{}^{7}\mathrm{Li}+{}^{1}\mathrm{H}$ | $0,0053_{5}$ | 0,0057 | 0,0055 |
| $^{7}\mathrm{Li}+{}^{1}\mathrm{H}\to2\,{}^{4}\mathrm{He}$ | $0,0182_{5}$ | 0,0184 | 0,0183 |
| $^{7}\mathrm{Li}+{}^{2}\mathrm{H}\to2\,{}^{4}\mathrm{He}+{}^{1}n$ | 0,0156 | 0,0150 | 0,0161 |
| $^{9}\mathrm{Be}+{}^{1}\mathrm{H}\to{}^{8}\mathrm{Be}+{}^{2}\mathrm{H}$ | 0,00051 | $^{8}\mathrm{Be}=8,0092$ | $^{8}\mathrm{Be}=8,0071$ |
| $^{9}\mathrm{Be}+{}^{1}\mathrm{H}\to{}^{6}\mathrm{Li}+{}^{4}\mathrm{He}$ | 0,0022 | 0,0066 | 0,0022 |
| $^{9}\mathrm{Be}+{}^{2}\mathrm{H}\to{}^{7}\mathrm{Li}+{}^{4}\mathrm{He}$ | $0,0077_{4}$ | 0,0123 | 0,0077 |
| $^{9}\mathrm{Be}+{}^{2}\mathrm{H}\to{}^{8}\mathrm{Be}+{}^{3}\mathrm{H}$ | 0,0048 | 0,0047 | 0,0047 |
| $^{9}\mathrm{Be}+{}^{2}\mathrm{H}\to{}^{10}\mathrm{Be}+{}^{1}\mathrm{H}$ | 0,0051 | $^{10}\mathrm{Be}=10,0162$ | $^{10}\mathrm{Be}=10,0149$ |
| $^{9}\mathrm{Be}+{}^{2}\mathrm{H}\to{}^{10}\mathrm{B}+{}^{1}n$ | 0,0053 | 0,0076 | 0,0054 |
| $^{9}\mathrm{Be}+{}^{2}n\to{}^{8}\mathrm{Be}+{}^{1}n$ | $-0,0016$ | $-0,0017$ | 0,0017 |
| $^{11}\mathrm{B}+{}^{1}\mathrm{H}\to3\,{}^{4}\mathrm{He}$ | 0,0090 | 0,0123 | 0,0088 |
| $^{11}\mathrm{B}+{}^{1}\mathrm{H}\to{}^{8}\mathrm{Be}+{}^{4}\mathrm{He}$ | 0,0091 | 0,0074 | 0,0086 |
| $^{10}\mathrm{B}+{}^{1}n\to{}^{7}\mathrm{Li}+{}^{4}\mathrm{He}$ | 0,0021 | 0,0047 | 0,0022 |
| $^{2}\mathrm{H}+{}^{2}\mathrm{H}\to{}^{3}\mathrm{He}+{}^{1}n$ | $0,0028_{5}$ | $^{3}\mathrm{He}=3,0163$ | $^{3}\mathrm{He}=3,0172$ |
| $^{2}\mathrm{H}+{}^{2}\mathrm{H}\to{}^{3}\mathrm{H}+{}^{1}\mathrm{H}$ | $0,0042_{5}$ | $^{3}\mathrm{H}=3,0152$ | $^{3}\mathrm{H}=3,0161$ |
For $x$ the following value is obtained: $x=0,000314$ mass units, amounting to approximately $1/4000$ of an Aston mass unit. In the fourth column of Table 1 are given the corrected masses of the elements obtained with this value of $x$. Bethe used another route to establish the corrected masses. Taking the mass of ${}^{4}\mathrm{He}$ equal to 4,00216, he calculated from the reaction
\[ {}^{11}_{5}\mathrm{B}+{}^{1}_{1}\mathrm{H}=3\,{}^{4}_{2}\mathrm{He} \]
the mass of ${}^{11}_{5}\mathrm{B}$ and then, passing through a series of intermediate nuclear reactions (7 reactions), was able to determine the mass of ${}^{16}\mathrm{O}$ relative to the above-indicated value of the mass of ${}^{4}\mathrm{He}$. For ${}^{16}\mathrm{O}$ a value equal to 15,9952 was obtained. The most-
the relative deviation ratio \({}^{4}\mathrm{He}:{}^{16}\mathrm{O}\) differs from the previously accepted value by \(3/10000\). In the fifth column of Table 1 the masses of the elements obtained with this correction taken into account are given. As the table shows, Bethe’s data agree rather well with those of Rutherford and others.
Confirmation of the correctness of the introduced corrections is provided by the circumstance that the energies of nuclear reactions, calculated from the new, corrected masses, agree better with the experimental data than do the energies calculated from mass-spectrographic data. This can be seen from Table 2.
Recently Aston \(^{4}\) carried out measurements of the masses of certain elements by means of a new method. The preliminary data of these measurements are given in the sixth column of Table 1. Their accuracy is not greater than 1 in 10,000. As can be seen from the table, there are great discrepancies between Aston’s new and old data, and precisely in the direction that follows from the data of Oliphant, Kempton, and Rutherford.
In conclusion, we note that the introduction of corrections to the masses of the elements resolves the question of the instability of the beryllium nucleus. According to mass-spectrographic data beryllium is unstable, since its mass (9.0155) is greater than the mass of two \(\alpha\)-particles and a neutron (\(8.0043 + 1.0080 = 9.0123\)). However, experimental investigations do not confirm the instability of beryllium. According to the corrected data beryllium is a stable element—its mass (9.0135) is less than the mass of two \(\alpha\)-particles and a neutron (\(8.0068 + 1.0083 = 9.0151\)).
L. Groshev
LITERATURE
- Oliphant; Kempton, Rutherford, Proc. Roy. Soc., 149, 406, 1935.
- Oliphant, Kempton, Rutherford, Proc. Roy. Soc., 150, 241, 1935.
- Bethe, Phys. Rev. 47, 633, 1935.
- Aston, Nature, 135, 541, 1935.