Nuclear Decay and Radioactivity (4E) - Chem & Physics

1. What is the relationship between half-life $t_{1/2}$ and decay constant $\lambda$?

   $t_{1/2}=\frac{\ln 2}{\lambda}$. Half-life inversely relates to the decay constant, where $ln 2$ arises from solving for half remaining nuclei.

2. What particle is emitted in $ a$ decay, written in nuclide notation?

   $^{4}_{2}\text{He}$ (alpha particle). Alpha particles are helium nuclei with 2 protons and 2 neutrons, ejected from heavy unstable nuclei.

3. Identify the daughter nuclide after $beta^-$ decay: $^{14}_{6}\text{C} \to \ ?$

   $^{14}_{7}\text{N}$. Beta-minus decay of carbon-14 yields nitrogen-14 by converting a neutron to a proton.

4. What particles are emitted in $beta^+$ decay in a standard nuclear equation?

   $e^+ + \nu_e$. Beta-plus decay emits a positron and neutrino to balance the conversion of a proton to a neutron.

5. What is the definition of radioactive (nuclear) decay in terms of nucleus stability and emissions?

   Spontaneous transformation of an unstable nucleus with particle and/or $ gamma$ emission. Radioactive decay stabilizes an unstable nucleus by spontaneously emitting alpha, beta, or gamma radiation to release excess energy.

6. Which radiation type has the highest ionizing power: $ a$, $ beta$, or $ gamma$?

   $\alpha$ (highest ionizing power). Alpha particles, with high charge and mass, deposit energy densely, causing greatest ionization per path length.

7. What shielding is typically sufficient to stop most $ a$ radiation?

   A sheet of paper or outer dead skin layer. Alpha particles lose energy rapidly in matter due to strong interactions, stopped by minimal barriers.

8. What is the emitted particle in electron capture, and what lepton is typically produced?

   An inner $e^-$ is captured; typically emits $\nu_e$. Electron capture involves absorbing an inner electron to convert a proton to a neutron, typically producing a neutrino.

9. What is the activity formula $A(t)$ in terms of $\lambda$ and $N(t)$?

   $A(t)=\lambda N(t)$. Activity equals the product of decay constant and remaining nuclei, representing the decay rate.

10. What shielding is typically sufficient to stop most $ beta$ radiation?

    Thin metal or plastic (e.g., aluminum). Beta particles, being lighter electrons, require denser materials to absorb their kinetic energy.

11. What changes in $A$ and $Z$ occur in $beta^-$ decay of $^{A}_{Z}X$?

    $A$ unchanged; $Z \to Z+1$. Beta-minus decay converts a neutron to a proton, increasing atomic number by 1 without changing mass.

12. What changes in $A$ and $Z$ occur in $beta^+$ (positron) emission of $^{A}_{Z}X$?

    $A$ unchanged; $Z \to Z-1$. Positron emission converts a proton to a neutron, decreasing atomic number by 1 while mass remains constant.

13. What changes in $A$ and $Z$ occur in $ gamma$ emission from an excited nucleus?

    No change: $A$ and $Z$ unchanged. Gamma emission releases excess energy from an excited nucleus without altering proton or neutron count.

14. What particles are emitted in $beta^-$ decay in a standard nuclear equation?

    $e^- + \bar{\nu}_e$. Beta-minus decay emits an electron and antineutrino to conserve charge, energy, and lepton number.

15. What shielding is typically required to significantly attenuate $ gamma$ radiation?

    Thick lead or concrete. Gamma rays demand high-density shielding to increase interaction probability and attenuate intensity.

16. What is the exponential decay law for remaining nuclei $N(t)$ using decay constant $\lambda$?

    $N(t)=N_0 e^{-\lambda t}$. The exponential law describes the statistical decrease in undecayed nuclei over time due to constant decay probability.

17. What is the activity as a function of time if initial activity is $A_0$?

    $A(t)=A_0 e^{-\lambda t}$. Activity follows exponential decay as it is proportional to the number of undecayed nuclei.

18. Identify the daughter nuclide after $ a$ decay: $^{238}_{92}\text{U} \to \ ?$

    $^{234}_{90}\text{Th}$. Alpha decay of uranium-238 produces thorium-234 by ejecting a helium-4 nucleus.

19. What is the relationship between mass number $A$, protons $Z$, and neutrons $N$?

    $A = Z + N$. The mass number $A$ equals the sum of protons $Z$ and neutrons $N$ in the nucleus.

20. What changes in $A$ and $Z$ occur in $ a$ decay of $^{A}_{Z}X$?

    $A \to A-4$ and $Z \to Z-2$. Alpha decay ejects a helium nucleus, reducing mass by 4 and protons by 2.

21. Which radiation type has the highest penetration through matter: $ a$, $ beta$, or $ gamma$?

    $\gamma$ (highest penetration). Gamma rays, being high-energy photons, interact least with matter, allowing deepest penetration.

22. What is the unit of activity in SI, and what does it measure physically?

    Becquerel (Bq) = $1$ decay per second. The becquerel quantifies radioactive decay rate in disintegrations per second for precise measurement.

23. What do the symbols $A$ and $Z$ represent in nuclide notation $^{A}_{Z}X$?

    $A$ = mass number; $Z$ = atomic number (protons). In nuclide notation, $A$ represents the total nucleons while $Z$ indicates the number of protons defining the element.

24. What changes in $A$ and $Z$ occur in electron capture by a nucleus $^{A}_{Z}X$?

    $A$ unchanged; $Z \to Z-1$. Electron capture transforms a proton into a neutron by absorbing an orbital electron, reducing atomic number by 1 with unchanged mass.

25. What is the half-life definition in terms of number of undecayed nuclei?

    Time for $N$ to decrease to $frac{1}{2}N_0$. Half-life measures the time required for half the radioactive nuclei to decay, reflecting probabilistic decay.

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