JEE Chemistry Nuclear Chemistry Notes Set 01

Radioactivity and Types of Radiation

Radioactivity is the spontaneous emission of particles or radiation (or both) from unstable nuclei.
1. Alpha particles are helium nuclei \( {}^4_2He \) with charge +2; they are the least penetrating (stopped by thin aluminium foil) but the most strongly ionising, and they travel only a few centimetres in air.
2. Beta particles are fast electrons \( {}^0_{-1}e \) with charge -1; they have moderate penetration and ionisation.
3. Gamma rays are high-energy electromagnetic radiation with no charge and no mass; they are the most penetrating and the least ionising.
4. Order of penetrating power: \( \gamma > \beta > \alpha \). Order of ionising power: \( \alpha > \beta > \gamma \).

Kinetics of Radioactive Decay

Radioactive decay is a first order process, independent of temperature, pressure or chemical state.
\[ -\frac{dN}{dt} = \lambda N, \qquad N = N_0e^{-\lambda t} \] 1. Activity \( A = \lambda N \). The SI unit is the becquerel (1 Bq = 1 disintegration per second). 1 curie = \( 3.7\times10^{10} \) dps and 1 rutherford = \( 10^6 \) dps.
2. Half life \( t_{1/2} = \dfrac{0.693}{\lambda} \). After n half lives the amount left is \( N_0/2^n \).
3. Average (mean) life \( \tau = \dfrac{1}{\lambda} = 1.44\,t_{1/2} \).
4. For a decay chain with parent half life much larger than daughter, or in series decay \( A \to B \to C \), the daughter reaches its maximum when \( t_{max} = \dfrac{\ln(\lambda_A/\lambda_B)}{\lambda_A-\lambda_B} \).
5. Parallel decay: \( \lambda = \lambda_1+\lambda_2 \), and the branching fraction of path 1 is \( \lambda_1/\lambda \). The partial half life of a path is \( 0.693/\lambda_i \).

Applications

1. Carbon dating: living matter has a constant ratio of C-14 to C-12 (about 1 in \( 10^{12} \)). After death the C-14 decays, so the age is \( t = \dfrac{2.303}{\lambda}\log\dfrac{A_0}{A} \). It is reliable up to about 30,000 years.
2. Rock dating: the age of an ore is found from the ratio of Pb-206 to U-238, using \( t = \dfrac{2.303}{\lambda}\log\dfrac{N_0}{N} \) with \( N_0 = N_U + N_{Pb} \).
3. Blood volume is found by injecting a radioactive tracer and measuring its diluted activity.

Nuclear Stability

1. Even-odd rule: nuclei with even numbers of protons and neutrons are the most numerous stable ones (about 165), odd-odd the fewest (about 5).
2. Magic numbers 2, 8, 20, 28, 50, 82 and 126 of protons or neutrons give specially stable nuclei, for example \( {}^4_2He \), \( {}^{16}_8O \), \( {}^{40}_{20}Ca \) and \( {}^{208}_{82}Pb \).
3. Neutron to proton ratio: stable light nuclei have n/p close to 1; it rises to about 1.5 for the heaviest stable nucleus Bi-209. No stable nucleus exists with Z greater than 83.
4. Binding energy is the energy needed to split a nucleus into nucleons: \( BE = \Delta m\times931.5 \) MeV when \( \Delta m \) is in amu. The binding energy per nucleon peaks near mass number 50 to 60 (Fe, Co, Ni), so fission of heavy nuclei and fusion of light nuclei both release energy.
5. Packing fraction \( = \dfrac{\text{atomic mass} - \text{mass number}}{\text{mass number}}\times10^4 \); a negative value indicates a stable nucleus.

Modes of Decay

1. Nuclei with n/p above the stability belt emit beta particles (a neutron changes to a proton): Z increases by 1, A unchanged.
2. Nuclei with n/p below the belt emit positrons or capture a K-shell electron (a proton changes to a neutron): Z decreases by 1, A unchanged.
3. Nuclei with A greater than about 210 emit alpha particles: A decreases by 4, Z by 2.
4. Gamma emission follows alpha or beta decay as the excited daughter nucleus drops to the ground state; A and Z do not change.
5. Number of particles emitted when a nucleus goes from \( {}^{A_1}_{Z_1}X \) to \( {}^{A_2}_{Z_2}Y \): \( \alpha = \dfrac{A_1-A_2}{4} \), and \( \beta = 2\alpha-(Z_1-Z_2) \).

Natural Disintegration Series

Thorium series (4n): Th-232 to Pb-208, 6 alpha and 4 beta. Neptunium series (4n+1): Pu-241 to Bi-209, artificial. Uranium series (4n+2): U-238 to Pb-206, 8 alpha and 6 beta. Actinium series (4n+3): U-235 to Pb-207, 7 alpha and 4 beta.

Nuclear Reactions

1. In nuclear reactions mass number and charge are conserved; new elements form, and the rate does not depend on temperature or catalysts.
2. Artificial transmutation was first achieved by Rutherford: \( {}^{14}_7N + {}^4_2He \to {}^{17}_8O + {}^1_1H \), written \( {}^{14}_7N(\alpha,p){}^{17}_8O \).
3. Fission: a heavy nucleus such as U-235 splits after absorbing a slow neutron into two medium nuclei, releasing 2 to 3 neutrons and about 200 MeV; for example \( {}^{235}_{92}U + {}^1_0n \to {}^{141}_{56}Ba + {}^{92}_{36}Kr + 3\,{}^1_0n \). A chain reaction has initiation, propagation and termination.
4. Fusion: light nuclei combine at very high temperature (about \( 10^6 \) K) to give a heavier nucleus, as in the sun and the hydrogen bomb.
5. A nuclear reactor has fuel (fissile U-235, Pu-239, U-233; fertile U-238 and Th-232 are converted to fissile Pu-239 and U-233 in breeder reactors), a moderator (heavy water, graphite) to slow neutrons, control rods (cadmium, boron) to absorb neutrons, and a coolant.
6. Artificial radioactivity was discovered by Irene Curie and F. Joliot, who produced radioactive phosphorus-30 by bombarding aluminium with alpha particles.