JEE Chemistry Nuclear Chemistry Notes Set 02

The Nucleus

The nucleus contains protons and neutrons (nucleons). The atomic number Z is the number of protons, the mass number A is the number of nucleons, and the number of neutrons is A - Z.
Isotopes have the same Z but different A; isobars have the same A but different Z; isotones have the same number of neutrons.
Nuclei are stable when the n/p ratio is suitable: about 1 for light nuclei, rising to about 1.5 for heavy ones. Nuclei with even numbers of protons and neutrons are most stable, and 'magic numbers' (2, 8, 20, 28, 50, 82, 126) confer extra stability.

Radioactivity

Radioactivity is the spontaneous emission of radiation from unstable nuclei. It is a nuclear property, unaffected by temperature, pressure or chemical combination.
Alpha particle: helium nucleus, charge +2, mass 4. Emission lowers A by 4 and Z by 2.
Beta particle: a fast electron formed when a neutron changes into a proton. Emission raises Z by 1 and leaves A unchanged.
Positron emission lowers Z by 1 with A unchanged. Gamma rays are high-energy electromagnetic radiation with no charge or mass.
Group displacement: after alpha emission the element moves two groups to the left; after beta emission one group to the right.

Radioactive Decay Kinetics

Decay is a first-order process: \( N = N_0 e^{-\lambda t} \) and \( \lambda = \dfrac{2.303}{t}\log\dfrac{N_0}{N} \).
Half-life: \( t_{1/2} = \dfrac{0.693}{\lambda} \). After n half-lives the amount left is \( N_0/2^{n} \), where \( n = t/t_{1/2} \).
Average life: \( \tau = 1/\lambda = 1.44\,t_{1/2} \).
Units of activity: 1 curie = \( 3.7\times10^{10} \) disintegrations per second; 1 becquerel = 1 disintegration per second; 1 rutherford = \( 10^{6} \) disintegrations per second.

Radioactive Series

The 4n (thorium) series ends in Pb-208, the (4n + 2) uranium series in Pb-206, the (4n + 3) actinium series in Pb-207, and the (4n + 1) neptunium series in Bi-209.
Number of alpha particles emitted = (change in A)/4; beta particles = 2 x (alpha particles) - (decrease in Z).

Artificial Transmutation and Nuclear Reactions

Bombarding a nucleus with particles (alpha, proton, deuteron, neutron) can change it into another nucleus. Notation: target(projectile, ejected particle)product, for example \( {}^{14}_{7}N(\alpha, p){}^{17}_{8}O \).
In every nuclear equation the mass numbers and the atomic numbers must each balance.
Carbon-14 is formed in the upper atmosphere by \( {}^{14}_{7}N + {}^{1}_{0}n \rightarrow {}^{14}_{6}C + {}^{1}_{1}H \). Its decay is used in radiocarbon dating, and the ratio of U-238 to Pb-206 is used to date rocks.

Mass Defect and Binding Energy

Mass defect: \( \Delta m = \) (sum of masses of free nucleons) - (mass of nucleus). Binding energy = \( \Delta m \times c^{2} \), and 1 a.m.u. is equivalent to 931.5 MeV.
Binding energy per nucleon is highest (about 8.8 MeV) near iron, so fission of heavy nuclei and fusion of light nuclei both release energy.
Nuclear fission: a heavy nucleus such as U-235 splits after capturing a neutron, releasing about 200 MeV and further neutrons (chain reaction). Nuclear fusion: light nuclei such as hydrogen combine at very high temperature, as in stars.

Worked Examples

Example 1. How many alpha and beta particles are emitted when \( {}^{238}_{92}U \) changes to \( {}^{206}_{82}Pb \)?
Answer:
Alpha particles = (238 - 206)/4 = 8. Charge: 92 - 16 + x = 82, so beta particles = 6.

Example 2. The half-life of a radioactive nuclide is 20 minutes. What fraction remains after 80 minutes?
Answer:
80/20 = 4 half-lives, so the fraction left = \( (1/2)^4 = 1/16 \).

Example 3. A sample shows 25% of the original C-14 activity. Find its age (\( t_{1/2} \) = 5730 years).
Answer:
25% = 1/4 = \( (1/2)^2 \), so two half-lives have passed: age = 11460 years.