Chapter 31, Problem 14P

(a)

To determine

To Complete: The nuclear reaction.

Answer to Problem 14P

  $p+P{\to }_{16}^{32}\text{S}+\gamma$

Explanation of Solution

Given:

The reaction is,

  $p+?{\to }_{16}^{32}\text{S}+\gamma$

The left side of the reaction has 16 protons and 32 nucleons. The right side has 1 proton.

Let the unknown element be X.

Thus, X should have 15 protons and 31 neutrons.

  $X=P$ .

Conclusion:

Therefore, thecomplete reaction is $p+P{\to }_{16}^{32}\text{S}+\gamma$ .

(b)

To determine

The Q value.

Answer to Problem 14P

  $8.35\text{MeV}$

Explanation of Solution

Given:

The reaction is $p+P{\to }_{16}^{32}\text{S}+\gamma$ .

  $\begin{array}{c}{m}_p= 1.00727647\text{ u}\end{array}$

  $\begin{array}{c}{m}_{P-31}=30.973762\text{u}\end{array}$

  $\begin{array}{c}{m}_{S-32}=31.972071\text{u}\end{array}$

Formula Used:

If the reaction is:

  $\begin{array}{l}A+B\to C\end{array}$

  $\begin{array}{c}Q=\left(m_A+m_B-m_C\right)c^2\end{array}$

Calculation:

The Q factor is calculated as,

  $\begin{array}{c}\text{Q=}\left[ 1.00727647+30.973762-31.972071\right]\left(931.5\frac{\text{MeV}}{{\text{c}}^{\text{2}}}\right){\text{c}}^{\text{2}}\end{array}$

  $\begin{array}{c}=8.35\text{MeV}\end{array}$

Conclusion:

Therefore, the Q values is $8.35\text{MeV}$ .