Chapter 10, Problem 5E

(a)

To determine

The complete nuclear reaction equation $\text{S}{\text{c}}^{\ast }\to \text{S}\text{c}+\_\_\_$.

Answer to Problem 5E

The complete nuclear reaction equation is $\text{S}{\text{c}}^{\ast }\to \text{S}\text{c}+\text{γ}$. This process is gamma decay.

Explanation of Solution

Total mass number of reactant is $46$. Mass number of product is shown as $46$. According to conservation of mass number, mass number of reactant is equal to mass number of product. Missing atom must have a mass number of $46-46=0$.

Total atomic number of reactant is $21$ and shown atomic number of product is $21$. According to conservation of atomic number, the atomic number of reactant and product must be equal. Missing atom must have atomic number of $21-21=0$.

Gamma rays have atomic number $0$ and mass number $0$. An unstable nucleus decyas through gamma decay with emission of gamma rays to form stable nucleus.

Conclusion:

Therefore, the complete nuclear reaction equation is $\text{S}{\text{c}}^{\ast }\to \text{S}\text{c}+\text{γ}$. This process is gamma decay.

(b)

To determine

The complete nucler reaction equation $\text{T}\text{h}\to \_\_\_+\text{H}\text{e}$.

Answer to Problem 5E

The complete nuclear reaction equation $\text{T}\text{h}\to \text{R}\text{a}+\text{H}\text{e}$. This process is alpha decay.

Explanation of Solution

Alpha decay is disintegration of heavy nucleus into lighter nucleus with emission of alpha particles or helium particles to stabilise itself.

Total mass number of reactant is shown as $232$. Total mass number of product is $4$. According to conservation of mass number, mass number of reactant is equal to mass number of product. Missing atom must have a mass number of $232-228=4$.

Total atomic number of reactant is shown as $90$ and total atomic number of product is $2$. According to conservation of atomic number, the atomic number of reactant and product must be equal. Missing atom must have atomic number of $90-2=88$.

The atom with atomic number $88$ and mass number $228$ is Radium atom.

Conclusion:

Therefore, the complete nuclear reaction equation $\text{T}\text{h}\to \text{R}\text{a}+\text{H}\text{e}$. This process is alpha decay.

(c)

To determine

The complete nuclear reaction equation $\text{S}\text{c}\to \text{T}\text{i}+\_\_\_$.

Answer to Problem 5E

The complete nuclear reaction equation is $\text{S}\text{c}\to \text{T}\text{i}+\text{e}$. This process is beta decay.

Explanation of Solution

Betadecay is disintegration of heavy nucleus into lighter nucleus with emission of beta particles or electrons to stabilise itself.

Total mass number of reactant is shown as $47$. Total mass number of product is $47$. According to conservation of mass number, mass number of reactant is equal to mass number of product. Missing atom must have a mass number of $47-47=0$.

Total atomic number of reactant is shown as $21$ and total atomic number of product is $22$. According to conservation of atomic number, the atomic number of reactant and product must be equal. Missing atom must have atomic number of $21-22=-1$.

Electrons are assigned a atomic number of $-1$ and mass number of $0$.

Conclusion:

Therefore, the complete nuclear reaction equation is $\text{S}\text{c}\to \text{T}\text{i}+\text{e}$. This process is beta decay.