Nuclear Chemistry

Nuclear chemistry is the study of reactions involving changes in atomic nuclei. Nuclear reactions involve protons, neutrons, electrons, and other elementary particles. Unlike chemical reactions, they are not restricted to the movement of electrons.

Nuclear Reactions

Nuclear Transmutation

Nuclear transmutation is a type of reaction where a chemical element or isotope is converted into another chemical element. It occurs in any process where the number of protons or neutrons in the nucleus of an atom is changed by bombardment with neutrons, protons, or other nuclei.

$$\ce{^14_7N + ^1_0n -> ^14_6C + ^1_1H}$$

Radioactive Decay

Radioactive decay is the process by which unstable atomic nuclei lose energy by radiation. Any material containing unstable nuclei is considered radioactive. The instability of the nucleus leads to the spontaneous emission of elementary particles and/or electromagnetic radiation.

$$\ce{ ^210_84Po -> ^206_82Pb + ^4_1He}$$

Nuclear Stability

At first glance, one could conclude that the atomic nuclei of all elements are unstable. The atomic nucleus has a very high density, ~10$^{14}$ g/cm$^3$. It contains neutrons and similarly charged protons that repel one another. The high density and large repulsive force between protons should lead to disintegration of the nucleus. However, short-range attractive forces between neutrons and protons stabilize the nucleus; thus, an increase in neutrons counteracts the strong repulsion between protons and creates a more stable nucleus.

A quantitative measure of nuclear stability is the nuclear binding energy - the energy required to disintegrate a nucleus into its components.

$$\ce{ ^209_83Bi -> 83^1_1H + 126^1_0n \quad \Delta E = ? }$$

Quantitatively, $\Delta E = \Delta mc^2$, where:

• $\Delta E$ = energy of products - energy of reactant
• $\Delta m$ = the mass defect, i.e. mass of products - mass of reactants
• c = speed of light, ~2.9979x10$^8$ m/s

Kinetics of Radioactive Decay

The rate at which an unstable nucleus decays can be measured using the following equation:

$$\ln \left( \frac{N_{0}}{Nt} \right) = \lambda t$$

Where:

• $t$ = time ($s$)
• $\lambda$ = rate constant ($s^{-1}$)
• $N_{0}$ and $N_{t}$ = number of radioactive nuclei at $t = 0$ and $t=t$, respectively

The half-life, $t_{1/2}$, of the reaction can be determined using the following equation:

$$t_{1/2} = \frac{\ln(2)}{\lambda}$$