Conservation of Nucleon Number and Other Laws

Through radioactive decay, nuclear fusion and nuclear fission, the number of nucleons (sum of protons and neutrons) is always held constant.

Learning Objective

Define the Law of Conservation of Nuclear Number

Key Points

The law of Conservation of Nuclear Number states that the sum of protons and neutrons among species before and after a nuclear reaction will be the same.
In radioactive decay, a proton can be converted to a neutron and a neutron can be converted to a proton (beta-decay).
Nuclear fusion and fission involve the conversion of matter to energy, but the matter that is converted is never a full nucleon.

Terms

fusion
A nuclear reaction in which nuclei combine to form more massive nuclei with the concomitant release of energy.
fission
The process of splitting the nucleus of an atom into smaller particles; nuclear fission.
nucleon
One of the subatomic particles of the atomic nucleus (i.e., a proton or a neutron).

Full Text

In physics and chemistry there are many conservation laws—among them, the Law of Conservation of Nucleon Number, which states that the total number of nucleons (nuclear particles, specifically protons and neutrons) cannot change by any nuclear reaction.

Radioactive Decay

Consider the three modes of decay. In gamma decay, an excited nucleus releases gamma rays, but its proton (Z) and neutron (A-Z) count remain the same:

$^A_ZN\rightarrow ^A_ZN+\gamma$.

In beta decay, a nucleus releases energy and either an electron or a positron. In the case of an electron being released, atomic mass (A) remains the same as a neutron is converted into a proton, raising atomic number by 1:

$^A_ZN\rightarrow ^A_{Z+1}N+e^-+ \nu$.

In the case of a positron being released, atomic mass remains constant as a proton is converted to a neutron, lowering atomic number by 1:

$^A_ZN\rightarrow ^A_{Z-1}N+e^++ \nu$.

Electron capture has the same effect on the number of protons and neutrons in a nucleus as positron emission.

Alpha decay is the only type of radioactive decay that results in an appreciable change in an atom's atomic mass. However, rather than being destroyed, the two protons and two neutrons an atom loses in alpha decay are released as a helium nucleus.

Nuclear Fission

Chain reactions of nuclear fission release a tremendous amount of energy, but follow the Law of Conservation of Nucleon Number. Consider, for example, the multistep reaction that occurs when a U-235 nucleus accepts a neutron, as in :

Nuclear fission of U-235

If U-235 is bombarded with a neutron (light blue small circe), the resulting U-236 produced is unstable and undergoes fission. The resulting elements (shown here as Kr-92 and Ba-141) do not contain as many nucleons as U-236, with the remaining three neutrons being released as high-energy particles, able to bombard another U-235 atom and maintain a chain reaction.

$^1_0n+^{235}_{92}U\rightarrow ^{236}_{92}U \rightarrow ^{144}_{56}Ba+ ^{89}_{36}Kr + 3 ^1_0n + \gamma$.

In each step, the total atomic mass of all species is a constant value of 236. This is the same with all fission reactions.

Nuclear Fusion

Finally, nuclear fusion follows the Law of Conservation of Nucleon Number. Consider the fusion of deuterium and tritium (both hydrogen isotopes):

$^2_1H+^3_1H \rightarrow ^4_2He + ^1_0n$.

It is well understood that the tremendous amounts of energy released by nuclear fission and fusion can be attributed to the conversion of mass to energy. However, the mass that is converted to energy is rather small compared to any sample, and never includes the conversion of a proton or neutron to energy. Thus, the number of nucleons before and after fission and fusion is always constant.

[ edit ]

Prev Concept

Quantum Tunneling

Medical Imaging and Diagnostics

Next Concept