the structure of atomic...

493

The Structure of Atomic Nuclei

By H. A. Wilson, F.R.S., Rice Institute, Houston, Texas

{Received September 17, 1935)

In a previous paper* it was shown that the energies of nuclear reactions are multiples of q =0-000415 in atomic weight units and that the atomic weights of the light elements may be supposed equal to N (1 + +where N and s are integers and bis a small quantity the same for all elements. In the reaction equations the terms N (1 + cancel out so that the reaction energies are given by nq = 'Esq. Thus the equation ,Be9 + jH1 = 4Be8 + XH2 + nq gives

9 (1 + b) + 33? + 1 + b + \9q = 8 (1 + b) + \lq+ 2 (1 + + 34 + nq,

so that 33 q + 19 q — 11 q + 34# + nq which gives 52 = 51 orn = 1. The number of independent reaction equations is two less than the number of elements involved so that two of the values of the energy integer s can be selected. In the previous paper the values of s for 2He+ and jH1 were taken to be 8 and 19 respectively and the values of s for the other elements were calculated by means of the reaction equations.

Any atom, of atomic number z and atomic weight integer may be supposed formed by the combination of z protons and — neutrons according to the reaction equation

z jR1 + (w — z) on1 = ZA W + E, (1)

where E denotes the energy of formation of the atom ,AW in atomic weight units. If zsw denotes the energy integer for .A"’ then equation (1) gives

z jS1 + (w — z)oS1 = zsw + E/q.

By means of this equation the energies of formation! may be calculated using the values of ,sw given in the previous paper. Table I gives the values of E/q obtained in this way.

* ‘ Proc. Roy. Soc.,’ A, vol. 152, p. 497 (1935).t The energies of formation obtained in this way are uniquely determined by the

reaction energies and are independent of the values chosen for the energy integers o f aHe4 and xHl.

VOL. CLIII.— A. (February 1, 1936.) 2 N

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494 H. A. Wilson

T able 1— E nergies of F ormation in T erms of as U nit

iH2 5 3 Li6 78 4Be10 160 80 16 312,H3 20 3Li7 96 6B>» 1612 He3 17 4 Be8 139 5Bn 1882He4 70 4 Be9 143 7N 14 255

The energy integers of N14 and O16 were taken equal to 18 and 0 respectively.

The energies of formation, of course, can also be calculated directly from the atomic weights but the values so obtained are probably not as reliable as those got from the reaction energies. The atomic weights calculated from the reaction energies give the same energies of formation as the reaction energies.

The energies of formation and reaction energies are expressed in terms of q as unit in this paper.

The equation (1) gives the atomic weights in terms of the atomic weights of oft1 and jH1. If we take qH1 = 1 00830 and jH1 = 1 -007885, this equation gives the same atomic weights as were obtained in the previous paper with 2He4 = 4 -00332.

Atoms regarded as combinations of neutrons and hydrogen atoms are somewhat analogous to ordinary chemical compounds of, for example, carbon and hydrogen. The difference is mainly that the energy of formation of an atom is much greater than the energy of formation of a chemical compound. The energy of formation of hydrocarbons can be calculated very approximately by supposing that the formation of each chemical bond between two atoms represents a definite amount of energy so it seems natural to try to explain the energies of formation of atoms out of neutrons and hydrogen atoms in a similar way.

The neutrons and protons may be supposed to attract each other when very near together so that the energy of formation should depend simply on the numbers of pairs of particles connected. Since the energies of formation are multiples of q the energies of formation of such pairs should also be multiples of q.

Such a theory, if valid, should enable the energies of formation of atoms to be calculated by assuming a suitable structure or arrangement and suitable energy values for the three sorts of pairs. Also the structures adopted should be such as to allow the observed reactions to occur with as little rearrangement of the neutrons and protons as possible. The energies of formation should also be as large as possible because an atom in which the particles could be rearranged so as to increase the energy of formation would be expected to change with emission of energy.



The Structure o f Nuclei 495

The energy of formation of 4H2 is 5 which suggests that the energy of a bond or connexion between a neutron and a proton should be 5. However, in the other atoms, with the exception of 2He3, a proton never appears to be connected to only one neutron but always to two or more neutrons or to another proton, and when a proton is connected to two or more neutrons the energy appears to be 10 for each connexion.

The energy of formation of 2He3 is 17. We may suppose that in 2He3 there are three bonds two between a neutron and a proton each with energy 5 as in 4H2 and one between the two protons with energy 7. Tn the other atoms the energy of a bond between two protons appears to be 21 or three times that in 2He3. The energy of formation of 4H3 is 20 and may be supposed to be that of two bonds between a proton and a neutron.

The energy of formation of 2He4 is 70 and we may suppose the four particles at the corners of a tetrahedron so that there are four proton- neutron bonds, one proton-proton bond, and one neutron-neutron bond. The proton-neutron bonds give 40 so if we take the energy of the proton- proton bond equal to 21 and that of the neutron-neutron bond equal to9 we get the required total of 70.

The energy of formation of 3Li8 is 78. We may suppose each proton connected to two neutrons giving energy 60 so that there should be two neutron-neutron bonds each with energy 9.

The energy of formation of sLi‘ is 96 or 18 more than for 3Li8. We therefore suppose 3Li7 to have four neutron-neutron bonds and six proton-neutron bonds giving 6 x 10 + 4 x 9 = 96.

The energy of formation of 4Be8 is 139 which is equal to 21 + 2 x 9 +10 x 10 and that of 4Be9 is 143 which is 7 x 9 + 8 x 10. The energy of formation of 4Be10is 160 which is 16 x 10, or 2 x 21 + 2 X 9 + 10 x 10.

Fig. 1 shows possible arrangements of the neutrons and protons in these atoms. A neutron is indicated by a small circle and a proton by a black disc.

It is possible that the energy of formation of 4Be8 is 140 instead of 139 and the value 140 is supported by the simple cubical arrangement in fig. 1 which gives 140 and may be regarded as two 2He4 atoms connected together.

The energy of formation of 4Be9 is smaller than might have been expected, and there is no very obvious reason why a neutron should not be connected to two of the neutrons in the cubical 4Be8 atom which would give a 4Be9 atom with energy of formation 158 and so atomic weight 9 00747 which is much smaller than the accepted value 9-0137. To explain why

2 n 2



496 H. A. Wilson

a 4Be9 atom with energy of formation 158 cannot be formed it is necessary to assume something analogous to valency. We may suppose, for example, that a neutron which is attached to two connected protons, as in a helium atom, cannot be attached to more than one other neutron. This would make the 4Be9 atom with energy of formation 158 impossible.

The energy of formation of 6B10 is 161 which is equal to 21 + 14 X 10, and that of 5BU is 188 which is 2 x 21 + 4 x 9 + 11 X 10. The energy of formation of oxygen 8Oie is 312 which is equal to 8 x 9 -f 24 x 10.

i , ■

9-----O O • O

j,H25 iH3 20

,Li6 78

4Be9 143

4Be8 140

4Be10 160

Fig. 2 shows possible arrangements of the neutrons and protons in 5B10, 5Bu, and 80 16.

Figs. 3, 4, 5, 6 show how the neutrons and protons may be supposed to be rearranged in a number of nuclear reactions. The reactions are numbered as in the list of 17 reactions given in the previous paper. In the initial state, the bonds which remain unchanged are represented by thick lines and those which disappear by thin lines. The new bonds to be formed are indicated by dotted lines.

It appears that the observed reactions can be explained by the assumed nuclear constitutions. Since the atoms have the correct energies the reaction energies must be correct also. The reactions (5), (8), (9), (16), and (17) not shown in figs. 3, 4, 5, 6 may be represented in the same way.



The Structure o f Atomic Nuclei 497

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jB10 161

5B“ 188

Fig. 2.

2 He4 + aHe4

Fig. 3.

(3)

(4)



498 H. A. Wilson

4Be» + 1H1 -> 2He4-f-3Li6 (7)

1H2 + 4B e«-*1H1 + 4Be1° (10)Fig. 4.

o * ' O4B e 9 + 1H 2 ^ 5B 10 + o « 1

0 —

4Be8 + on1 -> 4Be9

5B14 + 4Hl 3 2He4 Fig. 5.

(11)

( 12)

(13)




They are either so similar to those shown or so simple as not to be worth showing.

The reaction 8Oui + 1H2 -*■ 7N14 + 2He4 is shown in fig. 7. The two neutrons on the right-hand side of the N14 atom are assumed to be separated from the adjacent neutrons since otherwise the atomic weight

Fig. 6.(15)

tOl« + iH- -> 7N 14 + 2He4

Fig. 7.

of the N14 atom would be exactly 14. This makes the energy of formation of 7N14 equal to 255 and so 7s14 = 18 which gives 7N14 = 14-00747. This agrees nearly with Bethe’s* value which is 14-0076. The energy of the reaction is given by 0 + 34 = 18 + 8 + E, which gives E = 8.

* Bethe, ‘ Phys. Rev.,’ vol. 47, p. 634 (1935).



500 H. A. Wilson

If we suppose a helium atom 2He4 split off from an oxygen atom as in fig. 8 we get a carbon atom 6C12. If the bond shown dotted is present the 6C12 atom has energy of formation 234 and so atomic weight exactly 12. If the dotted bond is not present then the atom has energy of formation 225 and atomic weight 12-003735 which agrees well with Bethe’s

.O18 -* 6C12 + 2He4 Fig. 8.

value 12-0037. The energy of the reaction 6C12 + 2He4 -> 8Oie is given by9 + 8 = 0 + E which gives E = 17.

The atom 80 17 may be supposed to have the constitution shown in fig. 9. This gives 80 17 = 17 + 10 q=17-00415 which is slightly less than Bethe’s value 17-0040.

The reaction 0«4 + 7N14 -» 2He4 + -Bu is shown in fig. 10. The energy of the reaction is given by 18 + 20 = 8 + 27 + E, which gives E = 3.

Fluorine 9F19 may be supposed formed by adding one proton and two neutrons to 8O10 as shown in fig. 11. This makes the energy of formation of 9F19 equal to 371 which gives 9,s19 = 0 and 9F19 — 19 exactly.

If the helium atom on the right of the 9F19 atom is removed we get 7N15. This atom may be supposed to have the con

stitution shown in fig. 12, which makes its energy of formation 280 and its atomic weight 15-005395, which agrees well with Bethe’s value 15-0053.

The reaction 5BU + XH2 -> 6C12 + 0«4 is shown in fig. 13. This makes the energy of formation of 6C12 equal to 224 so that ev12 = 1 0 and the energy of the reaction is given by 34 + 27 = 20 + 10 + E which gives




E = 31. According to Lauritsen and Crane,* the energy of this reaction is 12-1 mV or 31-27.

The energy of formation 224 for 6C12 gives 6C12 = 12-00415 which is

9F19 371 Fig. 11.

r

~N15 280 Fig. 12.

I

1H2 + 5Bu ^ 0«i + 9C12 Fig. 13.

- . V i : . I ■ , . I

higher than Bethe’s 12-0037. If we suppose one of the neutron-neutron bonds removed and the proton-neutron bond, shown dotted in 6C12 added the energy of formation becomes 225 and the atomic weight 12-003735;

* ‘ Rep. Tnt. Conf. Nuclear Phys. London,’ p. 141 (1935).



502 H. A. Wilson

but this makes the energy of the reaction 32. We might have expected to have both the dotted bond and all six neutron-neutron bonds making the atomic weight exactly 12 but this makes the reaction energy much too large.

The reaction 9F19 + 1H1 -> 80 1B + 2He4 is shown in fig. 14. The energy of the reaction is given by 0 + 19 = 0 + 8 + E, which gives E = 11. This is less than the energy found by Henderson, Livingstone, and Lawrence,* which was about 17.

Fig. 14.

Another possible constitution of 9F19 is shown in fig. 15. This makes the energy of formation 367 so that 9s19 = 371 — 367 — 4, and aF19 = 19-00166. The energy of the reaction 9F19 + jH1 -> 8Oie + 2He4 is then given b y 4 + 1 9 = 0 + 8 + E which gives E = 15.

It does not seem to be possible to make the reaction energy equal to 17 without giving up the simple relation between the 80 16 and 9F19 atoms. The reaction 6C13 + 1H1 -> 5B10 + 2He4 is shown in fig. 16. We suppose that the neutron at A is displaced by the proton and that it then combines with the two protons B and C and the neutron D. The energy of formation of the 6C13 atom is 237, so that 6s13 = 254 - 237 = 17, and 6C13 - 13-007055, which is slightly greater than Bethe’s value 13 -0069. The energy of the reaction is given

by 17 + 19 = 34 + 8 + E, so that E = - 6.The neutrons and protons in many of the atoms considered may be

arranged in many ways with energies of formation less than that of the normal atoms. Atoms with such lower energies of formation are excited atoms and should change to normal atoms with the emission of gamma

* ‘ Rep. Int. Conf. Nuclear Phys. London,’ p. 125 (1935).



The Structure o f Nuclei 503

rays. When the energy levels of the atoms are known it may be possible to deduce the arrangements for such excited atoms. Fig. 17 shows several excited 4Be° atoms.

6C13 + xHl -> SB10 + 2He4 Fig. 16.

It appears that series of excited states with energies of formation differing by q may be possible. Series of energy levels with energy differences roughly equal to q have been observed with several light elements.

Since almost any energy of formation, within certain limits, can be obtained with some of the atoms it is clear that the fact that arrangements

, 0 ,

< £ >

141 142 4Be9

Fig. 17.

7 ^=7140

can be found having the correct energies of formation, for such atoms, should not be regarded as providing much support for the present theory. The way in which the assumed arrangements offer simple explanations of the observed reactions is of much greater weight.



504 E. O. Braaten and G. F. Clark

It is possible that other values of the bond energies with different arrangements could be found which would equally well explain the observed energies and reactions. The writer has tried several other sets of bond energies but was not able to find arrangements giving the correct energies of formation, of all the atoms considered, with them.

Summ ary

The energies of formation of several atoms, from neutrons and protons, are calculated from nuclear reaction energies. It is suggested that the energies of formation may be supposed due to the formation of bonds or connexions between the neutrons and protons. Arrangements of the neutrons and protons and bond energies are found which give the correct energies of formation. The observed reactions may be explained by means of the assumed nuclear arrangements or constitutions and the bond energies.

The Diffusion of Hydrogen through Copper

By E. O. B raaten and G. F. C la r k *

( Communicated by Sir John McLennan, F.R.S.—Received July 18, 1935)

Introduction

At temperatures higher than about 400° C, several observers have determined the rates of diffusion of hydrogen through copper, and only recently has a paper by Smithells and Ransley appeared, f giving measurements on diffusion as low as 225° C. Sieverts,$ Deming and Hendricks,! and Lombard! have shown that the copper tubes and plates used in the experiments at high temperatures tend to crystallize and become fissured, so that the measurements are of little value.

The adsorption of hydrogen by copper has been thoroughly studied over a large temperature range. Ward§ has shown that, at low temperatures, the immediate initial adsorption is followed by a slow solution of the hydrogen in the copper. Solution increases very rapidly with temperature, and

* Holder of Fellowship, Graduate School, University of Toronto, 1934-35.f 4 Proc. Roy. Soc.,’ A, vol. 150, p. 172 (1935).% See McBain, J. W., “ The Sorption of Gases by Solids,” p. 263.§ ‘ Proc. Roy. Soc.,’ A, vol. 133, p. 506 (1931).



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