Section 7.4: Nuclear Decay
Nuclear decay is the process by which an unstable nucleus loses energy by emitting radiation. Common types of decay include:
- Alpha decay (α): Emission of an alpha particle (2 protons, 2 neutrons).
- Beta decay (β): Conversion of a neutron to a proton with emission of an electron (β⁻) or positron (β⁺).
- Gamma decay (γ): Emission of high-energy photons without changing the number of protons or neutrons.
The activity of a radioactive sample decreases exponentially: \[ N(t) = N_0 e^{-\lambda t} \] where \( N_0 \) is initial number of nuclei, \( \lambda \) is decay constant, and \( t \) is time.
Example: Half-Life Calculation
A radioactive isotope has half-life 5 hours. Calculate the remaining fraction after 15 hours.
\( N = N_0 \left(\frac{1}{2}\right)^{t/T_{1/2}} = N_0 \left(\frac{1}{2}\right)^{15/5} = N_0 \left(\frac{1}{2}\right)^3 = \frac{N_0}{8} \)
Practice Problems
- Calculate the decay constant for a nuclide with half-life 10 days.
- A sample contains 1.0 × 10²⁴ nuclei. How many remain after two half-lives?
- Write balanced nuclear equations for alpha, beta, and gamma decay.
- Explain why gamma decay does not change the atomic number.
- Determine the activity of a sample containing 5.0 × 10²⁰ nuclei with decay constant 1.0 × 10⁻⁴ s⁻¹.