Question

part b: writing nuclear decay reactions: write equations for the following nuclear decay reactions. make sure that both mass numbers and atomic numbers are balanced on each side

1. decay of polonium - 218 by alpha (α) emission.
2. decay of carbon - 14 by beta (β -) emission.
3. the alpha decay of radon - 198
4. the beta (β -) decay of uranium - 237
5. the gamma decay of radium - 228 with alpha decay

Explanation:

Step1: Recall alpha - decay formula

In alpha - decay, the parent nucleus emits an alpha particle ($_{2}^{4}\text{He}$). The mass number of the parent nucleus decreases by 4 and the atomic number decreases by 2.

Step2: Write polonium - 218 alpha - decay equation

Polonium has atomic number 84. The equation is $_{84}^{218}\text{Po}
ightarrow_{82}^{214}\text{Pb}+_{2}^{4}\text{He}$.

Step3: Recall beta - decay formula

In beta - decay ($\beta^-$), a neutron in the nucleus is converted into a proton and an electron (beta particle $_{ - 1}^{0}\text{e}$). The mass number remains the same and the atomic number increases by 1.

Step4: Write carbon - 14 beta - decay equation

Carbon has atomic number 6. The equation is $_{6}^{14}\text{C}
ightarrow_{7}^{14}\text{N}+_{ - 1}^{0}\text{e}$.

Step5: Write radon - 198 alpha - decay equation

Radon has atomic number 86. The equation is $_{86}^{198}\text{Rn}
ightarrow_{84}^{194}\text{Po}+_{2}^{4}\text{He}$.

Step6: Write uranium - 237 beta - decay equation

Uranium has atomic number 92. The equation is $_{92}^{237}\text{U}
ightarrow_{93}^{237}\text{Np}+_{ - 1}^{0}\text{e}$.

Step7: Note on gamma - decay

Gamma decay does not change the mass number or atomic number of the nucleus. It is usually accompanied by other types of decay. If we assume the main decay is alpha - decay for radium - 228 (atomic number 88), the alpha - decay equation is $_{88}^{228}\text{Ra}
ightarrow_{86}^{224}\text{Rn}+_{2}^{4}\text{He}$. Gamma rays ($\gamma$) are often emitted during this process, but they do not affect the mass - number and atomic - number balance in the way alpha or beta particles do.

Answer:

1. $_{84}^{218}\text{Po}

ightarrow_{82}^{214}\text{Pb}+_{2}^{4}\text{He}$

1. $_{6}^{14}\text{C}

ightarrow_{7}^{14}\text{N}+_{ - 1}^{0}\text{e}$

1. $_{86}^{198}\text{Rn}

ightarrow_{84}^{194}\text{Po}+_{2}^{4}\text{He}$

1. $_{92}^{237}\text{U}

ightarrow_{93}^{237}\text{Np}+_{ - 1}^{0}\text{e}$

1. $_{88}^{228}\text{Ra}

ightarrow_{86}^{224}\text{Rn}+_{2}^{4}\text{He}$ (with possible $\gamma$ - ray emission)