Students will learn about radioactive decay and how to write nuclear equations.
Key Equations
- Atomic symbols like \begin{align*}^A_Z X \end{align*} are interpreted in the following way: \begin{align*}X\end{align*} is the symbol for the element involved. For example, \begin{align*}U\end{align*} is the symbol for the element uranium. \begin{align*}Z\end{align*} is the atomic number. \begin{align*}A\end{align*} is the atomic mass number, the total number of nucleons (protons and neutrons). A would be \begin{align*}235\end{align*} for uranium.
- The nuclear process is largely random in direction. Therefore, radiation strength decreases with distance by the inverse square of the distance (the \begin{align*}1/\mathit{r}^2\end{align*} law, which also holds for gravity, electric fields, light intensity, sound intensity, and so on.)
Guidance
- Alpha decay is the process in which an isotope releases a helium nucleus (\begin{align*}2\end{align*} protons and \begin{align*}2\end{align*} neutrons, \begin{align*}\frac{4}{2}\;\mathrm{He}\end{align*}) and thus decays into an atom with two less protons.
- Example: \begin{align*}\ ^{232}_{90} \;\mathrm{Th}\rightarrow\ ^{228}_{88}\;\mathrm{Ra}+\ ^{4}_{2}\;\mathrm{He}\end{align*}
Beta Decay
- Beta decay is the process in which one of the neutrons in an isotope decays, leaving a proton, electron and anti-neutrino. As a result, the nucleus decays into an atom that has the same number of nucleons, with one neutron replaced by a proton. (Beta positive decay is the reverse process, in which a proton decays into a neutron, anti-electron and neutrino.)
- Example: \begin{align*}\ ^{14}_{6}\;\mathrm{C}\rightarrow\ ^{14}_{7}\;\mathrm{N}+\ ^{ 0}_{-1}\;\mathrm{e}^-+\;\mathrm{v}\end{align*}
Gamma Decay
- Gamma decay is the process in which an excited atomic nucleus kicks out a photon and releases some of its energy. The makeup of the nucleus doesn’t change, it just loses energy. (It can be useful to think of this as energy of motion – think of a shuddering nucleus that only relaxes after emitting some light.)
- Example: \begin{align*}\ ^{137}_{56}\;\mathrm{Ba}^*\rightarrow\ ^{137}_{56}\;\mathrm{Ba+y}\end{align*}
Fission and Fusion
- Fission is the process in which an atomic nucleus breaks apart into two less massive nuclei. Energy is released in the process in many forms, heat, gamma rays and the kinetic energy of neutrons. If these neutrons collide with nuclei and induce more fission, then a runaway chain reaction can take place. Fission is responsible for nuclear energy and atom-bomb explosions: the fission of uranium acts as a heat source for the Earth’s molten interior.
- Example: \begin{align*}\ ^{1}\;\mathrm{n} + \ ^{235} \;\mathrm{U}\rightarrow\ ^{141}\;\mathrm{Ba} + \ ^{92}\;\mathrm{Kr}+3 ^{1}\;\mathrm{n}\end{align*}
- Fusion is the process in which two atomic nuclei fuse together to make a single nucleus. Energy is released in the form of nuclear particles, neutrons, and gamma-rays.
- Example: \begin{align*}\ ^{3}_{1}\;\mathrm{H} + \ ^{2}_{1}\;\mathrm{H} \rightarrow\ ^{4}_{2}\;\mathrm{He} + \ ^{1}_{0}\;\mathrm{n + y}\end{align*}
Watch this Explanation
Alpha Decay
Beta Decay
Time for Practice
- Which of the following is true for the following reaction? \begin{align*}\ ^{236}\;\mathrm{U} \rightarrow \ ^{90}\;\mathrm{Sr} + \ ^{143}\;\mathrm{Xe} + 3 ^{1}\;\mathrm{n}\end{align*}
- This is a fission reaction.
- This is a fusion reaction.
- This is not a valid reaction, because the equations don’t balance.
- You detect a high number of alpha particles every second when standing a certain distance from a radioactive material. If you triple your distance from the source, the number of alpha particles you detect will decrease. By what factor will it decrease?
- \begin{align*}\sqrt{3}\end{align*}
- \begin{align*}3\end{align*}
- \begin{align*}9\end{align*}
- \begin{align*}27\end{align*}
- It will stay the same.
- Write the nuclear equations \begin{align*}A \to B + C\end{align*} for the following reactions.
- The alpha decay of \begin{align*}^{219}\mathrm{Ra}\end{align*}.
- The beta decay of \begin{align*}^{158}\mathrm{Eu}\end{align*}.
- The beta decay of \begin{align*}^{53}\mathrm{Ti}\end{align*}.
- The alpha decay of \begin{align*}^{211}\mathrm{Bi}\end{align*}.
- Radium-226 undergoes alpha decay. What element is produced?
- Write the nuclear reaction for each of the processes described below:
- Calcium-45 decays to produce Scandium (Sc)
- undergoes alpha decay
- helium-3 is produced by beta decay of a certain nuclide
Answers to Selected Problems
- .
- .
- a. \begin{align*}^{219}{_{88}}\mathrm{Ra} \rightarrow ^{215}{_{86}}\mathrm{Rn} + ^{4}{_{2}}\mathrm{He}\end{align*} b. \begin{align*}^{158}{_{63}}\mathrm{Eu} \rightarrow ^{158}{_{64}}\mathrm{Gd} + ^{0}{_{-1}}e^-\end{align*} c. \begin{align*}^{53}{_{22}}\mathrm{Ti} \rightarrow ^{53}{_{23}}\mathrm{Va} + ^{0}{_{-1}}e^-\end{align*} d. \begin{align*}^{211}{_{83}}\mathrm{Bi} \rightarrow ^{207}{_{81}}\mathrm{Tl} + ^{4}{_{2}}\mathrm{He}\end{align*}
- Radon, Rn-222
- .