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 transformations and disintegrations of chemical elements bombarded with protons, deuterons, neutrons, or a l p h Nrticles.
having a unit mass like the proton, but no electric charge. The triton, or the nucleus of triple-weight
ITH a growing interest in artificial disiutegrations of atomic nuclei i t becomes desirable to have some simple graphical means for immediately 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 isotopes 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 it; 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 indicated 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 which carries a unit of positive electric charge. The deuteron, or the nucleus of heavy hydrogen, consists of hydrogen (tritium) is supposed to consist of a proton a proton and a neutron associated with it, the latter and two neutrons.
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The scale bar a t the left has three modifications of particles which contributes to the weight of the atom, helium nuclei marked on it. The lowest one is the but not to the charge in its nucleus or to the number of ordinary alpha particle which may be assumed to con- orbital electrons. Therefore, A - Z may be said to 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,
FIGURE2.-TEE A u r ~ r oD~E M O N S ~ A TTHE E S US5 SCALE
O F THE
represent the number of neutrons. The subscripts indicate 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 element. 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 deuterons (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 Be410is 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 B6Iois formed, with the emission of a neutron, no1. 7. Boron BE9is formed, with the emission of two neutrons. Of these theoretically possible transformations, those numbered 1, 3, 4, and 6 have been actually observed.'
is a purely hypothetical nucleus consisting of two protons. 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 ahsorption 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 neutrons, 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 atomic weight of an element is A and its atomic nun- ,RASETTI, F.,, ' ~ l of~nuclear ~ ~ physics," ~ t ~~ ~ ~ ~ t i ~ ~ - ~ ~ 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 numbers. It will be seen that these conditions are fulimpossible for some reasons outside the simple balance filled in the equation. The particular scale shown was of the constituents of the nuclei. After all, the scale built for the range of atomic weights of from 0 to 4 and gives only the "arithmetically" possible transforma- for atomic numbers from 0 to 2. It could be constructed for any other desired range. Since the loci of equal tions, and does not indicate the energy relations. In the same position of the scale, one may read the atomic numbers in the chart of isotopes are vertical results of bombarding BQ'O with protons, B P with lines, the same relationship is preserved on the scale. neutrons, B p with gamma rays, and so forth. Should The loci of equal atomic weights on the chart are fortyheavier bombarding particles be used than helium five degree diagonal lines slanting down to the right; nuclei, another scale may be constructed, or the same the same is true of the scale. The two points of diierence between the chart and the scale are as follows: scale marked with different symbols. (1) The atomic numbers increase to the right in the The foregoing scale is based on the general equation chart and to the left on the scale. A + a - b ~ ~ + P ~ - - f Y z + . -+Q: s (2) The atomic weights increase upward in the chart where X is an atom of the original bombarded isotope and downward on the scale. Because of these differences, the foregoing general and Y is the final product. P is the bombarding parequation is fulfilled: going in any direction from one ticle or radiation, and Q is the ejected particle or radiation. The subscripts and the superscripts indicate the point to another on the scale, the sum of the subatomic numbers and weights, respectively. The sum scripts read a t the two ends of a pin remains the same. of the atomic weights on both sides of the equation This is also true of the superscripts, and proves the must be the same, and so must be the sum of the atomic scale to be correct.
