31.4 Nuclear decay and conservation laws  (Page 7/27)

A nucleus in an excited state undergoes $\gamma$ decay, losing 1.33 MeV when emitting a $\gamma$ ray. In order to conserve energy in the reaction, what frequency must the $\gamma$ ray have?

${}_{95}^{241}\text{Am}$ 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.

For β decay, the nucleus releases a negative charge. In order for charge to be conserved overall, the nucleus must gain a positive charge, increasing its atomic number by 1, resulting in ${}_{96}^{241}\text{Cm.}$

A ${}_6^{14}\text{C}$ nucleus undergoes a decay process, and the resulting nucleus is ${}_7^{14}\text{N}$ . What is the value of the charge released by the original nucleus?

1. +1
2. 0
3. -1
4. -2

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

Identify the missing particle based upon conservation principles:

${}_7{}^{14}\text{N}+{}_2{}^4\text{H}\text{e}\to X+{}_8{}^{17}\text{O}$

1. ${}_1{}^2\text{H}$
2. ${}_1{}^1\text{H}$
3. ${}_6{}^{12}\text{C}$
4. ${}_6{}^{12}\text{C}$
5. ${}_4{}^8\text{B}\text{e}$

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

1. ${}_{92}{}^{238}\text{U}\to {}_{88}{}^{234}\text{R}\text{a}+{}_2{}^4\text{H}\text{e}$
2. ${}_{88}{}^{223}\text{R}\text{a}\to {}_{82}{}^{209}\text{P}\text{b}+{}_6{}^{14}\text{C}$
3. ${}_6{}^{14}\text{C}\to {}_7{}^{14}\text{N}+e^{-}+{\overline{v}}_{\text{e}}$
4. ${}_{12}{}^{24}\text{M}\text{g}\to {}_{11}{}^{23}\text{N}\text{a}+e^{+}+v_{\text{e}}$