Complete each of the following nuclear decay equations by determining the mass number and atomic number of the following isotopes after they have emitted either a beta particle, an alpha particle or gamma radiation. Use the periodic table to assist you in identifying the remaining particle. a. $$ \begin{array}{r}210 \ 82 \ \mathrm{~Pb}\end{array} ightarrow \quad{ }_{-1}^{0} \mathrm{e}+ $$ $$ \qquad $$ 1. $$ \begin{array}{lll}\frac{1}{\vdots} & \mathrm{~T} \ \vdots & ightarrow & 0 \gamma+ \ \vdots & & 0\end{array} $$ $$ \qquad $$ b. $$ { }_{84}^{209} \mathrm{PO} ightarrow{ }_{82}^{205} \mathrm{~Pb}+ $$ $$ \qquad $$ j. $$ { }_{90}^{234} \mathrm{Th} ightarrow{ }_{91}^{234} \mathrm{~Pa}+ $$ $$ \qquad $$ c. $$ { }_{92}^{239} \mathrm{U} ightarrow \quad{ }_{-1}^{0} \mathrm{e}+ $$ $$ \qquad $$ d. $$ { }_{92}^{238} \mathrm{U} ightarrow{ }_{2}^{4} \mathrm{He}+ $$ $$ \qquad $$ k. $$ { }_{94}^{239} \mathrm{Pu} ightarrow \quad{ }_{2}^{4} \mathrm{He}+ $$ $$ \qquad $$ I. $$ { }_{13}^{27} \mathrm{Al} ightarrow{ }_{2}^{4} \mathrm{He}+ $$ $$ \qquad $$ e. $$ \begin{array}{r}228 \ 93 \ \mathrm{~Np}\end{array} ightarrow \quad-1 \mathrm{e}+ $$ $$ \qquad $$ f. $$ \begin{array}{l}42 \ 19\end{array} \mathrm{~K} \quad{ }_{19}^{42} \mathrm{~K}+ $$ $$ \qquad $$ m. $$ { }_{13}^{27} \mathrm{Al} ightarrow{ }_{-1}^{0} \mathrm{e}+ $$ $$ \qquad $$ g. $$ { }_{88}^{226} \mathrm{Ra} ightarrow{ }_{2}^{4} \mathrm{He}+ $$ $$ \qquad $$ ก. $$ { }_{4}^{9} \mathrm{Be} ightarrow{ }_{4}^{9} \mathrm{Be}+ $$ $$ \qquad $$

Question

Complete each of the following nuclear decay equations by determining the mass number and atomic number of the following isotopes after they have emitted either a beta particle, an alpha particle or gamma radiation. Use the periodic table to assist you in identifying the remaining particle. a. $$ \begin{array}{r}210 \ 82 \ \mathrm{~Pb}\end{array} ightarrow \quad{ }_{-1}^{0} \mathrm{e}+ $$ $$ \qquad $$ 1. $$ \begin{array}{lll}\frac{1}{\vdots} & \mathrm{~T} \ \vdots & ightarrow & 0 \gamma+ \ \vdots & & 0\end{array} $$ $$ \qquad $$ b. $$ { }_{84}^{209} \mathrm{PO} ightarrow{ }_{82}^{205} \mathrm{~Pb}+ $$ $$ \qquad $$ j. $$ { }_{90}^{234} \mathrm{Th} ightarrow{ }_{91}^{234} \mathrm{~Pa}+ $$ $$ \qquad $$ c. $$ { }_{92}^{239} \mathrm{U} ightarrow \quad{ }_{-1}^{0} \mathrm{e}+ $$ $$ \qquad $$ d. $$ { }_{92}^{238} \mathrm{U} ightarrow{ }_{2}^{4} \mathrm{He}+ $$ $$ \qquad $$ k. $$ { }_{94}^{239} \mathrm{Pu} ightarrow \quad{ }_{2}^{4} \mathrm{He}+ $$ $$ \qquad $$ I. $$ { }_{13}^{27} \mathrm{Al} ightarrow{ }_{2}^{4} \mathrm{He}+ $$ $$ \qquad $$ e. $$ \begin{array}{r}228 \ 93 \ \mathrm{~Np}\end{array} ightarrow \quad-1 \mathrm{e}+ $$ $$ \qquad $$ f. $$ \begin{array}{l}42 \ 19\end{array} \mathrm{~K} \quad{ }_{19}^{42} \mathrm{~K}+ $$ $$ \qquad $$ m. $$ { }_{13}^{27} \mathrm{Al} ightarrow{ }_{-1}^{0} \mathrm{e}+ $$ $$ \qquad $$ g. $$ { }_{88}^{226} \mathrm{Ra} ightarrow{ }_{2}^{4} \mathrm{He}+ $$ $$ \qquad $$ ก. $$ { }_{4}^{9} \mathrm{Be} ightarrow{ }_{4}^{9} \mathrm{Be}+ $$ $$ \qquad $$

UpStudy AI · Accepted Answer

To complete the nuclear decay equations, we need to determine the mass number and atomic number of the resulting isotopes after the emission of particles. Let's go through each equation step by step.

### a. $$ \begin{array}{r}210 \ 82 \ \mathrm{~Pb}\end{array} ightarrow \quad{ }_{-1}^{0} \mathrm{e}+ $$
- **Decay Type**: Beta decay (emission of a beta particle).
- **Mass Number**: Remains the same (210).
- **Atomic Number**: Decreases by 1 (from 82 to 81).
- **Resulting Isotope**: $$ \begin{array}{r}210 \ 81 \ \mathrm{~Tl}\end{array} $$

### b. $$ { }_{84}^{209} \mathrm{PO} ightarrow{ }_{82}^{205} \mathrm{~Pb}+ $$
- **Decay Type**: Alpha decay (loss of 2 protons and 4 nucleons).
- **Mass Number**: $$ 209 - 4 = 205 $$.
- **Atomic Number**: $$ 84 - 2 = 82 $$.
- **Resulting Isotope**: $$ \begin{array}{r}205 \ 82 \ \mathrm{~Pb}\end{array} $$

### j. $$ { }_{90}^{234} \mathrm{Th} ightarrow{ }_{91}^{234} \mathrm{~Pa}+ $$
- **Decay Type**: Beta decay (emission of a beta particle).
- **Mass Number**: Remains the same (234).
- **Atomic Number**: Increases by 1 (from 90 to 91).
- **Resulting Isotope**: $$ \begin{array}{r}234 \ 91 \ \mathrm{~Pa}\end{array} $$

### c. $$ { }_{92}^{239} \mathrm{U} ightarrow \quad{ }_{-1}^{0} \mathrm{e}+ $$
- **Decay Type**: Beta decay.
- **Mass Number**: Remains the same (239).
- **Atomic Number**: Decreases by 1 (from 92 to 91).
- **Resulting Isotope**: $$ \begin{array}{r}239 \ 91 \ \mathrm{~Np}\end{array} $$

### d. $$ { }_{92}^{238} \mathrm{U} ightarrow{ }_{2}^{4} \mathrm{He}+ $$
- **Decay Type**: Alpha decay.
- **Mass Number**: $$ 238 - 4 = 234 $$.
- **Atomic Number**: $$ 92 - 2 = 90 $$.
- **Resulting Isotope**: $$ \begin{array}{r}234 \ 90 \ \mathrm{~Th}\end{array} $$

### k. $$ { }_{94}^{239} \mathrm{Pu} ightarrow \quad{ }_{2}^{4} \mathrm{He}+ $$
- **Decay Type**: Alpha decay.
- **Mass Number**: $$ 239 - 4 = 235 $$.
- **Atomic Number**: $$ 94 - 2 = 92 $$.
- **Resulting Isotope**: $$ \begin{array}{r}235 \ 92 \ \mathrm{~U}\end{array} $$

### I. $$ { }_{13}^{27} \mathrm{Al} ightarrow{ }_{2}^{4} \mathrm{He}+ $$
- **Decay Type**: Alpha decay.
- **Mass Number**: $$ 27 - 4 = 23 $$.
- **Atomic Number**: $$ 13 - 2 = 11 $$.
- **Resulting Isotope**: $$ \begin{array}{r}23 \ 11 \ \mathrm{~Na}\end{array} $$

### e. $$ \begin{array}{r}228 \ 93 \ \mathrm{~Np}\end{array} ightarrow \quad-1 \mathrm{e}+ $$
- **Decay Type**: Beta decay.
- **Mass Number**: Remains the same (228).
- **Atomic Number**: Decreases by 1 (from 93 to 92).
- **Resulting Isotope**: $$ \begin{array}{r}228 \ 92 \ \mathrm{~U}\end{array} $$

### f. $$ \begin{array}{l}42 \ 19\end{array} \mathrm{~K} \quad{ }_{19}^{42} \mathrm{~K}+ $$
- **Decay Type**: No decay (remains the same).
- **Mass Number**: Remains the same (42).
- **Atomic Number**: Remains the same (19).
- **Resulting Isotope**: $$ \begin{array}{r}42 \ 19 \ \mathrm{~K}\end{array} $$

### m. $$ { }_{13}^{27} \mathrm{Al} ightarrow{ }_{-1}^{0} \mathrm{e}+ $$
- **Decay Type**: Beta decay.
- **Mass Number**: Remains the same (27).
- **Atomic Number**: Decreases by 1 (from 13 to 12).
- **Resulting Isotope**: $$ \begin{array}{r}27 \ 12 \ \mathrm{~Mg}\end{array} $$

### g. $$ { }_{88}^{226} \mathrm{Ra} ightarrow{ }_{2}^{4} \mathrm{He}+ $$
- **Decay Type**: Alpha decay.
- **Mass Number**: $$ 226 - 4 = 222 $$.
- **Atomic Number**: $$ 88 - 2 = 86 $$.
- **Resulting Isotope**: $$ \begin{array}{r}222 \ 86 \ \mathrm{~Rn}\end{array} $$

### ก. $$ { }_{4}^{9} \mathrm{Be} ightarrow{ }_{4}^{9} \mathrm{Be}+ $$
- **Decay Type**: No decay (remains the same).
- **Mass Number**: Remains the same (9).
- **Atomic Number**: Remains the same (4).
- **Resulting Isotope**: $$ \begin{array}{r}9 \ 4 \ \mathrm{~Be}\end{array} $$

### Summary of Results
1. $$ \begin{array}{r}210 \ 81 \ \mathrm{~Tl}\end{array} $$
2. $$ \begin{array}{r}205 \ 82 \ \mathrm{~Pb}\end{array} $$
3. $$ \begin{array}{r}234 \ 91 \ \mathrm{~Pa}\end{array} $$
4. $$ \begin{array}{r}239 \ 91 \ \mathrm{~Np}\end{array} $$
5. $$ \
Here are the completed nuclear decay equations with the resulting isotopes: a. $$ \begin{array}{r}210 \ 81 \ \mathrm{~Tl}\end{array} $$ b. $$ \begin{array}{r}205 \ 82 \ \mathrm{~Pb}\end{array} $$ j. $$ \begin{array}{r}234 \ 91 \ \mathrm{~Pa}\end{array} $$ c. $$ \begin{array}{r}239 \ 91 \ \mathrm{~Np}\end{array} $$ d. $$ \begin{array}{r}234 \ 90 \ \mathrm{~Th}\end{array} $$ k. $$ \begin{array}{r}235 \ 92 \ \mathrm{~U}\end{array} $$ I. $$ \begin{array}{r}23 \ 11 \ \mathrm{~Na}\end{array} $$ e. $$ \begin{array}{r}228 \ 92 \ \mathrm{~U}\end{array} $$ f. $$ \begin{array}{r}42 \ 19 \ \mathrm{~K}\end{array} $$ m. $$ \begin{array}{r}27 \ 12 \ \mathrm{~Mg}\end{array} $$ g. $$ \begin{array}{r}222 \ 86 \ \mathrm{~Rn}\end{array} $$ ก. $$ \begin{array}{r}9 \ 4 \ \mathrm{~Be}\end{array} $$

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