Question

Assuming that about 200 MeV of energy is released per fission of ₉₂U²³⁵nuclei, then the mass of U²³⁵ consumed per day in fission reactor of power 1 megawatt will be approximately:

• A. 10^–2g
• B. 1 g
• C. 100 g
• D. 10,000 g

Answer 1

Answer: (B)

1 g

Answer 2

Power P of fission reactor.

P = 10⁶ watt = 10⁶ joule/sec

Time = t = 1 day = 24 × 36 × 10² sec

Energy produced, U = Pt

or U = 10⁶ × 24 × 36 × 10²

= 24 × 36 × 10⁸ joule

Energy released per fission of U²³⁵

200 MeV = 32 × 10 ^–12 J

Number of U²³⁵ atoms used

= $\frac { 24 \times 36 \times 10 ^ { 8 } } { 32 \times 10 ^ { - 12 } }$ = 27 × 10²⁰

Mass of 6 × 10²³ atoms of U²³⁵ = 235 g Mass of 27 × 10²⁰ atoms of U²³⁵

= $\left( \frac { 235 } { 6 \times 10 ^ { 23 } } \right)$ (27 × 10²⁰)

= 1.058 g $\simeq$ 1 g