The combustion of a single molecule of methane produces about 10 eV of energy. A methane molecule has a mass of 16 amu. The fission of a uranium-235 atom produces about 189 MeV of energy. Based on these numbers, about what mass of methane will produce as much energy as a single gram of uranium-235? (One MeV is equal to one million eV.) A. 19 grams of methane. B. 304 grams of methane. C. 71.4 kilograms of methane. D. 1,287 kilograms of methane.
Answers
The correct answer is option D. 1,287 kilograms of methane.
Explanation :
one mole of U-235 = 235 grams
=> 1 gram of U-235 = 1/235 moles
1 mole of U-235 = 6.023 x 10²³ atoms
=> 1/235 moles of U-235 = 6.023 x 10²³/235 atoms
= 25.6 x 10²⁰ atoms
one atom of U-235 gives = 189 x 10⁶ eV energy
=> 25.6 x 10²⁰ atoms of U-235 gives = 25.6 x 10²⁰ x 189 x 10⁶
= 4.8 x 10²⁹ eV energy
One methane molecule produces = 10 eV energy
=> To produce 4.8 x 10²⁹ eV energy , no. of molecules required
= 4.8 x 10²⁸
6.032 x 10²³ molecules of methane = 16 gms
=> 4.8 x 10²⁸ molecules of methane = 16 x 4.8 x 10²⁸/ 6.032 x 10²³ gms
= 12.75 x 10⁵ gms
= 1275 kilograms of methane
≅ 1287 kilograms of methane
Hence option D) 1287 kilograms of methane will give the same amount of energy as 1 gram of U-235 .