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Q7P

Expert-verifiedFound in: Page 1331

Book edition
10th Edition

Author(s)
David Halliday

Pages
1328 pages

ISBN
9781118230718

**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. **

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

The generated energy, *P* =1 W

The released energy, *Q* =200 MeV

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

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

Calculate the fission ratio.

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

$R=\frac{1\mathrm{W}}{200\mathrm{MeV}}\phantom{\rule{0ex}{0ex}}R=\frac{1\mathrm{W}}{200\times {10}^{6}\mathrm{eV}}\phantom{\rule{0ex}{0ex}}R=\frac{1\mathrm{W}}{200\times {10}^{6}\times 1.6\times {10}^{19}\mathrm{J}}\phantom{\rule{0ex}{0ex}}R=\frac{1}{3.2\times {10}^{11}}$

Solve further as,

$R=\frac{{10}^{11}}{3.2}\phantom{\rule{0ex}{0ex}}R=\frac{10\times {10}^{10}}{3.2}\phantom{\rule{0ex}{0ex}}R=3.12\times {10}^{10}{s}^{-1}$

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

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