Question

Verify the Q values reported in Eqs. 43-13, 43-14, and 43-15. The needed masses are

$\begin{array}{cccc}{}^{\mathbf{1}}\mathbf{H}& \mathbf{1}\mathbf{.}\mathbf{007825}\mathbf{u}& {}^{\mathbf{4}}\mathbf{He}& \mathbf{4}\mathbf{.}\mathbf{002603}\mathbf{u}\\ {}^{\mathbf{2}}\mathbf{H}& \mathbf{2}\mathbf{.}\mathbf{014102}\mathbf{u}& \mathbf{n}& \mathbf{1}\mathbf{.}\mathbf{008665}\mathbf{u}\\ {}^{\mathbf{3}}\mathbf{H}& \mathbf{3}\mathbf{.}\mathbf{016049}\mathbf{u}& \mathbf{}& \mathbf{}\end{array}$

Short answer

The Q values are verified.

Step-by-step solution

Describe the expression for energy

The expression for energy is given by,

$\mathit{Q}\mathbf{=}\mathbf{-}\mathbf{∆}\mathit{m}{\mathit{c}}^{\mathbf{2}}$

Here, Q is the energy release in a reaction,$\mathbf{∆}\mathit{m}$ is the mass difference between the parent nuclei and the daughter nuclei, and c is the velocity of light.

Verify the Q values

For the first reaction, the energy equation will be as follows.

$Q=\left(2m_{2H}-m_{3H}-m_n\right)c^2.........\left(1\right)$

Substitute all the known values in equation (1).

$$\begin{gathered} Q=\left[2\left(2.014102u\right)-3.016049u-1.008665u\right]\left(931.5MeV/u\right) \\ =3.25MeV \end{gathered}$$

For the second reaction, the energy equation will be as follows.

$Q=\left(2m_{2H}-m_{3H}-m_{1H}\right)c^2.........\left(2\right)$

Substitute all the known values in equation (2).

$$\begin{gathered} Q=\left[2\left(2.014102u\right)-3.016049u-1.007825u\right]\left(931.5MeV/u\right) \\ =4.03MeV \end{gathered}$$

For the third reaction, the energy equation will be as follows.

$Q=\left(m_{2H}-m_{3H}-m_{He}-m_n\right)c^2.........\left(3\right)$

Substitute all the known values in equation (3).

$$\begin{gathered} Q=\left[2\left(2.014102u\right)-3.016049u-1.002603u-1.008665\right]\left(931.5MeV/u\right) \\ =17.59MeV \end{gathered}$$

The calculated Q values are same as the given in equations.

Therefore, the Q values are verified.