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Radioactivity: Understanding Nuclear Decay and Its Applications
What Is Radioactivity?
Radioactivity is the spontaneous emission of radiation from unstable atomic nuclei as they decay into more stable forms.
Types of Nuclear Decay
Alpha Decay (\(\alpha\))
Alpha particles (\(2 \, \text{protons} + 2 \, \text{neutrons}\)) are emitted from the nucleus.
Example:
\[ ^{238}_{92}\text{U} \rightarrow ^{234}_{90}\text{Th} + ^{4}_{2}\alpha \]
Beta Decay (\(\beta\))
- Beta-minus (\(\beta^-\)) decay: A neutron turns into a proton, emitting an electron and an antineutrino.
\[ n \rightarrow p + e^- + \overline{\nu}_e \] - Beta-plus (\(\beta^+\)) decay: A proton turns into a neutron, emitting a positron and a neutrino.
\[ p \rightarrow n + e^+ + \nu_e \]
Gamma Radiation (\(\gamma\))
High-energy electromagnetic radiation emitted when a nucleus transitions to a lower energy state.
Half-Life and Radioactive Decay
The half-life (\(T_{1/2}\)) is the time it takes for half of a radioactive sample to decay.
Formula:
\[ N = N_0 \left(\frac{1}{2}\right)^{\frac{t}{T_{1/2}}} \]
Example: A \(100 \, \text{g}\) sample of a radioactive isotope has a half-life of \(5 \, \text{hours}\). Find the remaining amount after \(10 \, \text{hours}\):
- \(t/T_{1/2} = 10/5 = 2\)
- \(N = 100 \cdot \left(\frac{1}{2}\right)^2 = 25 \, \text{g}\)
Applications of Radioactivity
Medicine
- Radiotherapy: Treating cancer with gamma rays.
- Imaging: Using radioactive tracers in PET scans.
Energy Production
- Nuclear reactors use fission to generate electricity.
Archaeology
- Radiocarbon dating determines the age of ancient artifacts.
Safety Precautions and Risks
- Use shielding materials like lead or concrete.
- Minimize exposure time.
- Store radioactive materials securely.
Practice Questions
- A radioactive sample has a half-life of \(3 \, \text{days}\). If \(200 \, \text{g}\) of the sample decays, how much remains after \(9 \, \text{days}\)?
- Explain how gamma radiation is used in medicine.
- Describe the difference between alpha, beta, and gamma radiation.