TUNE. 1939 283

A SCALE for PREDICTING NUCLEAR TRANSFORMATIONS

VLADIMIR KARAPETOFF

Cornell University, Ithaca. New York

A nine-point scale is described which being placed on a chart of isotopes permits one to predict nuclear trans- formations and disintegrations of chemical elements bom- barded with protons, deuterons, neutrons, or a l p h Nrticles.

W ITH a growing interest in artificial disiutegra- tions of atomic nuclei i t becomes desirable to have some simple graphical means for immedi-

ately ascertaining theoretically what product or products may be expected when a given isotope of an element is bombarded with such particles as protons, neutrons, deuterons, or alpha particles. The simple device shown in the three figures serves this purpose.

It is made of a piece of celluloid in the form of a double H, and i t has nine points spaced a t the same distance as the adjacent elements on the chart of iso- topes with which i t is to be used. A deuteron D, or Hla, that is, the nucleus of a heavy hydrogen atom, is marked in the center of the device. Ordinary hydrogen nucleus, or proton, HI1, is marked a t the point above i t ; and the triple-weight isotope of hydrogen nucleus, H13, a t the point below it. All these three nuclei have the same atomic number, 1, indicated by the subscript. Their atomic weights are 1, 2, 3, respectively, as in- dicated by the superscripts. The nuclei and not the atoms are understood in this notation, in so far as the scale is concerned. The proton is a unit of atomic mass

having a unit mass like the proton, but no electric charge. The triton, or the nucleus of triple-weight

which carries a unit of positive electric charge. The deuteron, or the nucleus of heavy hydrogen, consists of a proton and a neutron associated with it, the latter and two neutrons.

hydrogen (tritium) is supposed to consist of a proton

The scale bar a t the left has three modifications of helium nuclei marked on it. The lowest one is the ordinary alpha particle which may be assumed to con- sist of two protons and two neutrons, thus giving an atomic weight of four and the atomic number two. Its isotope, He?, probably consists of two protons and a neutron. The substance marked on top of the bar, Hez2,

FIGURE 2.-TEE Aur~ro~ DEMONS~ATES THE US5 OF THE SCALE

is a purely hypothetical nucleus consisting of two pro- tons. If such a substance exists its logical place would be a t that point.

The three symbols on the right-hand bar of the scale refer to entities with the atomic number 0, that is, with no electric charge. Their atomic weights are 0, 1, and 2, respectively. The upper symbol refers to a pulse of gamma rays emitted as a result of an ahsorp- tion of a bombarding particle by the atom with which i t comes into collision. The middle symbol, nll, signifies a neutron, and the lower symbol represents two neu- trons, or a neutron of double atomic weight, if such a particle is ever found to exist.

The chart of isotopes is plotted in the usual manner against atomic numbers as abscissas. The number of neutrons in the nucleus is used as ordinates. If the

particles which contributes to the weight of the atom, but not to the charge in its nucleus or to the number of orbital electrons. Therefore, A - Z may be said to

represent the number of neutrons. The subscripts in- dicate the atomic number, being the same in any one column, and the superscripts denote the atomic weights, these being different for the isotopes of the same ele- ment. The most abundant and stable isotope of each element is represented by a solid black dot.

In Figure 1 a part of the chart of isotopes is shown in perspective under the scale, as an example. The atom to be bombarded and the bombarding particle are first brought into coincidence. Let the beryllium isotope of atomic weight 9 be bombarded with deu- terons (HI2). The scale is placed with its HI2 point over Be2 on the chart. W e then read the following possibilities:

1. Lithium L i j is formed, with the emission of an alpha-particle (Hez4).

2. Lithium L38 is formed with the emission of a helium ion, Hep3.

3. Beryllium Be410 is formed, with the emission of a proton, HI1.

4. Beryllium BeP is formed, with the emission of a triton, or triple-weight hydrogen ion, H13.

5. The bombarding deuteron is combined with the beryllium atom, forming a boron atom, Bsl1, with the emission of a gamma-ray pulse.

6. Boron B6Io is formed, with the emission of a neu- tron, no1.

7. Boron BE9 is formed, with the emission of two neutrons.

Of these theoretically possible transformations, those numbered 1, 3, 4, and 6 have been actually observed.'

atomic weight of an element is A and its atomic nun- ,RASETTI, F., , ' ~ l ~ ~ ~ ~ t ~ of nuclear physics," ~ ~ ~ ~ t i ~ ~ - ~ ~ l l . ber Z, the difference of the two gives the number of Inc., New York City, 1936, p. 245.

The others either have not been observed or may be impossible for some reasons outside the simple balance of the constituents of the nuclei. After all, the scale gives only the "arithmetically" possible transforma- tions, and does not indicate the energy relations.

In the same position of the scale, one may read the results of bombarding BQ'O with protons, B P with neutrons, B p with gamma rays, and so forth. Should heavier bombarding particles be used than helium nuclei, another scale may be constructed, or the same scale marked with different symbols.

The foregoing scale is based on the general equation A + a - b

~ ~ + P ~ - - f Y z + . - s +Q: where X is an atom of the original bombarded isotope and Y is the final product. P is the bombarding par- ticle or radiation, and Q is the ejected particle or radi- ation. The subscripts and the superscripts indicate the atomic numbers and weights, respectively. The sum of the atomic weights on both sides of the equation must be the same, and so must be the sum of the atomic

numbers. It will be seen that these conditions are ful- filled in the equation. The particular scale shown was built for the range of atomic weights of from 0 to 4 and for atomic numbers from 0 to 2. It could be constructed for any other desired range. Since the loci of equal atomic numbers in the chart of isotopes are vertical lines, the same relationship is preserved on the scale. The loci of equal atomic weights on the chart are forty- five degree diagonal lines slanting down to the right; the same is true of the scale. The two points of diier- ence between the chart and the scale are as follows:

(1) The atomic numbers increase to the right in the chart and to the left on the scale.

(2) The atomic weights increase upward in the chart and downward on the scale.

Because of these differences, the foregoing general equation is fulfilled: going in any direction from one point to another on the scale, the sum of the sub- scripts read a t the two ends of a pin remains the same. This is also true of the superscripts, and proves the scale to be correct.