36. prepare a table comparing the three types of radioactive decay we examined in section 13.1. include a…

Explanation:

Step1: Identify the three types of radioactive decay

Common types are alpha decay, beta decay (beta - minus and sometimes beta - plus/positron emission can be considered, but often beta - minus is the main beta decay type taught initially), and gamma decay. But since the problem refers to Section 13.1, we assume the three types are alpha, beta (beta - minus), and gamma (though gamma is more of an energy release after decay, but still a type of radioactive decay process).

Step2: Gather information for each type

Alpha Decay:

• Particle emitted: Alpha particle ($\alpha$), which is a helium - 4 nucleus, i.e., $_{2}^{4}\text{He}$ (has 2 protons and 2 neutrons).
• Effect on N (neutron number) and Z (proton number): The parent nucleus has Z protons and N neutrons. After alpha decay, the daughter nucleus has $Z - 2$ protons and $N - 2$ neutrons. So Z decreases by 2, N decreases by 2.
• Example: Uranium - 238 (${92}^{238}\text{U}$) undergoes alpha decay to form thorium - 234 (${90}^{234}\text{Th}$). The reaction is ${92}^{238}\text{U}\rightarrow{90}^{234}\text{Th}+_{2}^{4}\text{He}$

Beta - Minus Decay:

• Particle emitted: Beta - minus particle ($\beta^{-}$), which is an electron ($_{- 1}^{0}\text{e}$).
• Effect on N and Z: In beta - minus decay, a neutron in the nucleus decays into a proton, an electron, and an antineutrino ($\overline{\nu}_{e}$). So the number of protons (Z) increases by 1, and the number of neutrons (N) decreases by 1 (since a neutron is converted to a proton).
• Example: Carbon - 14 (${6}^{14}\text{C}$) undergoes beta - minus decay to form nitrogen - 14 (${7}^{14}\text{N}$). The reaction is ${6}^{14}\text{C}\rightarrow{7}^{14}\text{N}+{-1}^{0}\text{e}+\overline{\nu}{e}$

Gamma Decay:

• Particle emitted: Gamma ray ($\gamma$), which is a high - energy photon (has no mass and no charge, $_{0}^{0}\gamma$).
• Effect on N and Z: Gamma decay occurs after alpha or beta decay when the daughter nucleus is in an excited state. It releases energy in the form of gamma rays, but does not change the number of protons (Z) or neutrons (N) of the nucleus.
• Example: After the beta - decay of cobalt - 60 (${27}^{60}\text{Co}$) to nickel - 60 (${28}^{60}\text{Ni}$), the nickel - 60 nucleus is often in an excited state and undergoes gamma decay, emitting gamma rays. The initial beta - decay is ${27}^{60}\text{Co}\rightarrow{28}^{60}\text{Ni}+{-1}^{0}\text{e}+\overline{\nu}{e}$, and then the excited ${28}^{60}\text{Ni}^*$ emits a gamma ray: ${28}^{60}\text{Ni}^*\rightarrow_{28}^{60}\text{Ni}+\gamma$

Step3: Create the table

Type of Radioactive Decay	Particle Emitted	Effect on Z (Proton Number) and N (Neutron Number)	Example
Alpha Decay	Alpha particle ($_{2}^{4}\text{He}$)	Z decreases by 2, N decreases by 2	${92}^{238}\text{U}\rightarrow{90}^{234}\text{Th}+_{2}^{4}\text{He}$ (Uranium - 238 decaying to Thorium - 234)
Beta - Minus Decay	Beta - minus particle ($_{-1}^{0}\text{e}$)	Z increases by 1, N decreases by 1	${6}^{14}\text{C}\rightarrow{7}^{14}\text{N}+{-1}^{0}\text{e}+\overline{\nu}{e}$ (Carbon - 14 decaying to Nitrogen - 14)
Gamma Decay	Gamma ray ($\gamma$)	No change in Z or N	${28}^{60}\text{Ni}^*\rightarrow{28}^{60}\text{Ni}+\gamma$ (Excited Nickel - 60 emitting a gamma ray)

Answer:

The table comparing the three types of radioactive decay (alpha, beta - minus, and gamma) is as follows:

Type of Radioactive Decay	Particle Emitted	Effect on Z (Proton Number) and N (Neutron Number)	Example
Alpha Decay	Alpha particle ($_{2}^{4}\text{He}$)	Z decreases by 2, N decreases by 2	${92}^{238}\text{U}\rightarrow{90}^{234}\text{Th}+_{2}^{4}\text{He}$
Beta - Minus Decay	Beta - minus particle ($_{-1}^{0}\text{e}$)	Z increases by 1, N decreases by 1	${6}^{14}\text{C}\rightarrow{7}^{14}\text{N}+{-1}^{0}\text{e}+\overline{\nu}{e}$
Gamma Decay	Gamma ray ($\gamma$)	No change in Z or N	${28}^{60}\text{Ni}^*\rightarrow{28}^{60}\text{Ni}+\gamma$

(Note: If the three types in Section 13.1 are different, the table can be adjusted accordingly. For example, if beta - plus decay is included instead of or along with beta - minus, the information for beta - plus (positron emission, ${+1}^{0}\text{e}$) would be: Z decreases by 1, N increases by 1, and an example like ${11}^{22}\text{Na}\rightarrow_{10}^{22}\text{Ne}+{+1}^{0}\text{e}+\nu{e}$ (Sodium - 22 decaying to Neon - 22) can be used.)