Question

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

Options

• 10^-2 g

• 1 g

• 100 g

• 10,000 g

Answer 1

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

Explanation:

Power P of fission reactor.

P = 10⁶ watt = 10⁶ joule/s

Time = t = 1 day

= 24 × 36 × 10² s

The energy produced, U = Pt

or U = 10⁶ × 24 × 36 × 10²

= 24 × 36 × 10⁸ joule

The energy released per fission of U²³⁵

200 MeV = 32 × 10^-12 J

A number of U²³⁵ atoms was used.

= `(24 xx 36 xx 10^8)/(32 xx 10^-12)`

= `27 xx 10^20`

Mass of 6 × 10²³ atoms of U²³⁵ = 235 g

Mass of 27 × 10²⁰ atoms of U²³⁵

= `(235/(6 xx 10^23))(27 xx 10^20)`

= 1.058 g ≅ 1 g