31.4 Nuclear Decay and Conservation Laws

$_{95}^{241} \text{Am}$ is commonly used in smoke detectors because its α decay process provides a useful tool for detecting the presence of smoke particles. When $_{95}^{241} \text{Am}$ undergoes α decay, what is the resulting nucleus? If $_{95}^{241} \text{Am}$ were to undergo β decay, what would be the resulting nucleus? Explain each answer.

Explain why the overall charge of the nucleus is increased by +1 during the β decay process.

Are the following reactions possible? For each, explain why or why not.

1. ${}_{92}^{238}{\text{U}} \rightarrow {}_{88}^{234}{\text{R}} \text{a} + {}_{2}^{4}{\text{H}} \text{e}$
2. ${}_{88}^{223}{\text{R}} \text{a} \rightarrow {}_{82}^{209}{\text{P}} \text{b} + {}_{6}^{14}{\text{C}}$
3. ${}_{6}^{14}{\text{C}} \rightarrow {}_{7}^{14}{\text{N}} + e^{-} + \left(\bar{v}\right)_{\text{e}}$
4. ${}_{12}^{24}{\text{M}} \text{g} \rightarrow {}_{11}^{23}{\text{N}} \text{a} + e^{+} + v_{\text{e}}$

In the following eight problems, write the complete decay equation for the given nuclide in the complete $_{Z}^{A} X_{N}$ notation. Refer to the periodic table for values of $Z$.

$\beta^{- }$ decay of $^{3} \text{H}$ (tritium), a manufactured isotope of hydrogen used in some digital watch displays, and manufactured primarily for use in hydrogen bombs.

In the following eight problems, write the complete decay equation for the given nuclide in the complete $_{Z}^{A} X_{N}$ notation. Refer to the periodic table for values of $Z$.

$\beta^{+ }$ decay of $^{\text{50}} \text{Mn}$.

In the following eight problems, write the complete decay equation for the given nuclide in the complete $_{Z}^{A} X_{N}$ notation. Refer to the periodic table for values of $Z$.

Electron capture by $^{7} \text{Be}$.

In the following eight problems, write the complete decay equation for the given nuclide in the complete $_{Z}^{A} X_{N}$ notation. Refer to the periodic table for values of $Z$.

$\alpha$ decay of $^{\text{210}} \text{Po}$, the isotope of polonium in the decay series of $^{\text{238}} \text{U}$ that was discovered by the Curies. A favorite isotope in physics labs, since it has a short half-life and decays to a stable nuclide.

In the following four problems, identify the parent nuclide and write the complete decay equation in the $_{Z}^{A} X_{N}$ notation. Refer to the periodic table for values of $Z$.

$\beta^{- }$ decay producing $^{\text{137}} \text{Ba}$. The parent nuclide is a major waste product of reactors and has chemistry similar to potassium and sodium, resulting in its concentration in your cells if ingested.

In the following four problems, identify the parent nuclide and write the complete decay equation in the $_{Z}^{A} X_{N}$ notation. Refer to the periodic table for values of $Z$.

$\alpha$ decay producing $^{\text{228}} \text{Ra}$. The parent nuclide is nearly 100% of the natural element and is found in gas lantern mantles and in metal alloys used in jets ($^{\text{228}} \text{Ra}$ is also radioactive).

In the following four problems, identify the parent nuclide and write the complete decay equation in the $_{Z}^{A} X_{N}$ notation. Refer to the periodic table for values of $Z$.

When an electron and positron annihilate, both their masses are destroyed, creating two equal energy photons to preserve momentum. (a) Confirm that the annihilation equation $e^{+ } + e^{- } \rightarrow \gamma + \gamma$ conserves charge, electron family number, and total number of…

In the following four problems, identify the parent nuclide and write the complete decay equation in the $_{Z}^{A} X_{N}$ notation. Refer to the periodic table for values of $Z$.

Confirm that charge, electron family number, and the total number of nucleons are all conserved by the rule for $\beta^{- }$ decay given in the equation $_{Z}^{A} X_{N} \rightarrow _{Z + 1}^{A} \text{Y}_{N - 1} + \beta^{- } + \left(\bar{\nu}\right)_{e}$. To do this, identify the values of each before and after the decay.

In the following four problems, identify the parent nuclide and write the complete decay equation in the $_{Z}^{A} X_{N}$ notation. Refer to the periodic table for values of $Z$.

Confirm that charge, electron family number, and the total number of nucleons are all conserved by the rule for electron capture given in the equation $_{Z}^{A} X_{N} + e^{- } \rightarrow _{Z - 1}^{A} \text{Y}_{N + 1} + \nu_{e}$. To do this, identify the values of each before and after the capture.

In the following four problems, identify the parent nuclide and write the complete decay equation in the $_{Z}^{A} X_{N}$ notation. Refer to the periodic table for values of $Z$.

(a) Write the complete $\alpha$ decay equation for $^{\text{226}} \text{Ra}$.

(b) Find the energy released in the decay.

In the following four problems, identify the parent nuclide and write the complete decay equation in the $_{Z}^{A} X_{N}$ notation. Refer to the periodic table for values of $Z$.

(a) Write the complete $\beta^{- }$ decay equation for the neutron. (b) Find the energy released in the decay.

In the following four problems, identify the parent nuclide and write the complete decay equation in the $_{Z}^{A} X_{N}$ notation. Refer to the periodic table for values of $Z$.

Calculate the energy released in the $\beta^{+ }$ decay of $^{\text{22}} \text{Na}$, the equation for which is given in the text. The masses of $^{\text{22}} \text{Na}$ and $^{\text{22}} \text{Ne}$ are 21.994434 and 21.991383 u, respectively.

In the following four problems, identify the parent nuclide and write the complete decay equation in the $_{Z}^{A} X_{N}$ notation. Refer to the periodic table for values of $Z$.

(a) Calculate the energy released in the $\alpha$ decay of $^{\text{238}} \text{U}$.

(b) What fraction of the mass of a single $^{\text{238}} \text{U}$ is destroyed in the decay? The mass of $^{\text{234}} \text{Th}$ is 234.043593 u.

(c) Although the fractional mass loss is large for a single nucleus, it is difficul…

In the following four problems, identify the parent nuclide and write the complete decay equation in the $_{Z}^{A} X_{N}$ notation. Refer to the periodic table for values of $Z$.

(a) Write the complete reaction equation for electron capture by $^{\text{15}} \text{O}$.

(b) Calculate the energy released.