Question

What is the Qof the following fusion process?

${\mathbf{}}_{\mathbf{1}}^{\mathbf{2}}\mathbf{H}\mathbf{+}{\mathbf{}}_{\mathbf{1}}^{\mathbf{1}}\mathbf{H}\mathbf{\to }{\mathbf{}}_{\mathbf{2}}^{\mathbf{3}}\mathbf{He}\mathbf{+}\mathbf{photo}\mathbf{}\mathbf{n}$

Here are some atomic masses.

${\mathbf{}}_{\mathbf{1}}^{\mathbf{2}}\mathbf{H}\mathbf{}\mathbf{2}\mathbf{.}\mathbf{014102}\mathbf{u}\mathbf{}{\mathbf{}}_{\mathbf{1}}^{\mathbf{1}}\mathbf{H}\mathbf{}\mathbf{1}\mathbf{.}\mathbf{007825}\mathbf{u}\mathbf{}$

Short answer

The Q value of the given fusion process is 5.49 MeV .

Step-by-step solution

Write the given data

1. The given fusion process,${}_1^2\mathrm{H}+{}_1^1\mathrm{H}\to {}_2^3\mathrm{He}+\mathrm{photo}\mathrm{n}$
2. Atomic masses of the atoms in the fusion process are given.

 Step 2: Determine the concept of Q-value

The Q-value of the fusion process is the amount of energy that is either absorbed or released during the process. Thus, it describes the integration process for a fusion process that involves the binding of two nuclei.

Formula:

The Q-value for a fusion process with energy being released,

$\mathrm{Q}=∆{\mathrm{mc}}^2$ …… (i)

Here,${\mathrm{c}}^2=931.5\frac{\mathrm{MeV}}{\mathrm{u}}$

Determine the Q-value of the fusion process

From the given fusion process, the Q-value or the energy released by the fusion of hydrogen and a deuteron nucleus is obtained by equation (i) as follows:

$\mathrm{Q}=-\left({\mathrm{m}}_{\mathrm{He}}-{\mathrm{m}}_{{\mathrm{H}}^2}-{\mathrm{m}}_{{\mathrm{H}}^1}\right){\mathrm{c}}^2$

Solve further as:

$$\begin{gathered} \mathrm{Q}=-\left(3.016029\mathrm{u}-2.014102\mathrm{u}-1.007825\mathrm{u}\right)\left(931.5\frac{\mathrm{MeV}}{\mathrm{u}}\right) \\ =5.49\mathrm{MeV} \end{gathered}$$

Hence, the required Q-value is 5.49 MeV.