Question

At what rate must ${}^{\mathbf{235}}\mathbf{U}$nuclei undergo fission by neutron bombardment to generate energy at the rate of 1.00 W? Assume that Q=200 MeV.

Short answer

The rate at which nuclei undergo fission by neutron bombardment. $3.12\times {10}^{10}{\mathrm{s}}^{-1}$.

Step-by-step solution

Given data

The generated energy, P =1 W

The released energy, Q =200 MeV

Determine the formulas to calculate the rate at which nuclei undergo fission by neutron bombardment.

The expression to calculate the fission ratio is given as follows.

$\mathbf{R}\mathbf{=}\frac{\mathbf{P}}{\mathbf{Q}}$ ...(i)

Calculate the rate at which nuclei undergo fission by neutron bombardment.

Calculate the fission ratio.

Substitute 1W forP and 200 MeV for into equation (i).

$$\begin{gathered} R=\frac{1\mathrm{W}}{200\mathrm{MeV}} \\ R=\frac{1\mathrm{W}}{200\times {10}^6\mathrm{eV}} \\ R=\frac{1\mathrm{W}}{200\times {10}^6\times 1.6\times {10}^{19}\mathrm{J}} \\ R=\frac{1}{3.2\times {10}^{11}} \end{gathered}$$

Solve further as,

$$\begin{gathered} R=\frac{{10}^{11}}{3.2} \\ R=\frac{10\times {10}^{10}}{3.2} \\ R=3.12\times {10}^{10}{s}^{-1} \end{gathered}$$

Hence the rate at which nuclei undergo fission by neutron bombardment $3.12\times {10}^{10}{\mathrm{s}}^{-1}$.