High School

Burning one metric ton (1000 kg) of coal can yield energy of \(3.30 \times 10^{10} \, \text{J}\). Fission of one nucleus of uranium-235 yields an average of approximately 208 MeV. What mass of uranium produces the same energy as 1.4 metric tons of coal?

A) 0.007 kg
B) 70 kg
C) 700 kg
D) 7000 kg

Answer :

Final answer:

a) The mass of uranium that produces the same energy as 1.4 metric tons of coal is 0.007 kg.

Explanation:

To find the mass of uranium that produces the same energy as 1.4 metric tons of coal, we can set up a proportion using the given energy values:

(Mass of Uranium) / (Energy produced by Uranium) = (Mass of Coal) / (Energy produced by Coal)

Plugging in the values:

(Mass of Uranium) / (208 MeV) = (1.4 metric tons) / (3.3 x 10^10 J)

Cross multiplying and solving for the mass of uranium:

(Mass of Uranium) = (208 MeV) * (1.4 metric tons) / (3.3 x 10^10 J)

Calculating:

Mass of Uranium = 0.007 kg

Therefore, the mass of uranium that produces the same energy as 1.4 metric tons of coal is 0.007 kg.

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