Question

A nuclear power plant generates electric power of 200 MW using the nuclear fusion of U-235. How much uranium is consumed in a day to produce the electric power, if one U-235 nucleus produces 190 MeV of energy?

• A. $444\text{g}$
• B. $235\text{g}$
• C. $222\text{g}$
• D. $105\text{g}$

Answer 1

Answer: (C)

$222\text{g}$

Given:
One uranium-235 nucleus releases 190 MeV of energy during its fission.
$1MeV=1.6\times {10}^{-13}J$

$⟹190MeV=190\times 1.6\times {10}^{-13}J$

$=3.04\times {10}^{-11}J$

Electric power generated, $P=200MW$
Electric energy generated in an hour, $E=200\times {10}^6\times 3600=7.2\times {10}^{11}J$

The number of U-235 nuclei needed to release an energy of $7.2\times {10}^{11}J=\frac{7.2\times {10}^{11}}{3.04\times {10}^{-11}}$
$=2.3684\times {10}^{22}$ nuclei

Mass of $6.023\times {10}^{23}$ uranium nuclei = $235\text{g}$

Mass of $2.3684\times {10}^{22}$ uranium nuclei = $\frac{235}{6.023\times {10}^{23}}\times 2.3684\times {10}^{22}$

$=9.2408\text{g}$ per hour

For a day, the uranium consumed = $9.2408gh{r}^{-1}\times 24hr=221.78\text{g}$
$\approx 222\text{g}$