Chapter 31, Problem 51GP

(a)

To determine

The other reaction product.

Answer to Problem 51GP

The other reaction product is $\text{C}$

Explanation of Solution

Given:

Bombardment of $\text{B}\text{e}$ with the alpha particles.

Calculation:

Now, the bombardment of the $\text{B}\text{e}$ with the alpha particle can be given by the reaction as follows:

  $\text{B}\text{e}+\text{H}\text{e}\to \text{n}+?$

According to the statement, we need to find the missing reaction product in the reaction.

Total number of protons is given as: $4+2=6$

Total number of nucleons is given as: $9+4=13$

Both sides of the reaction must be balance according to the law of conservation. So, the number of protons and number of nucleons of the missing reaction product can be given by:

  $\begin{array}{l}6-0=6\\ 13-1=12\end{array}$

So, the reaction product will be: $\text{C}$

Hence, the reaction will be: $\text{B}\text{e}+\text{H}\text{e}\to \text{n}+\text{C}$

Conclusion:

Hence, the other reaction product is $\text{C}$

(b)

To determine

Q-value of the reaction.

Answer to Problem 51GP

The Q-value of the reaction is $\mathrm{Q}=5.7\text{ MeV}$

Explanation of Solution

Given:

Bombardment of $\text{B}\text{e}$ with the alpha particles.

Calculation:

The Q-value of the reaction can be calculated as follows:

  $\begin{array}{l}\mathrm{Q}=\left({\mathrm{m}}_{\mathrm{B}\mathrm{e}}+{\mathrm{m}}_{\mathrm{a}\mathrm{l}\mathrm{p}\mathrm{h}\mathrm{a}}+{\mathrm{m}}_{\mathrm{n}}+{\mathrm{m}}_{\mathrm{n}}\right)\\ \mathrm{Q}=\left(9.012182+4.002603+1.008665+12.0107\right)\left(931.5\right)\text{MeV}\\ \mathrm{Q}=5.7\text{ MeV}\end{array}$

Conclusion:

The Q-value of the reaction is $\mathrm{Q}=5.7\text{ MeV}$