Nuclear Decay and Radioactivity (4E) - MCAT Chemical and Physical Foundations of Biological Systems

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.

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

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

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

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

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

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

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

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

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

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

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

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.

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

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

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

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

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

$A$ 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.

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

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

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

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

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.