The energy released per fission of nucleus of ²⁴⁰X is 200 MeV. The energy released if all the atoms in 120g of pure ²⁴⁰X undergo fission is ____________ × 10²⁵ MeV.
(Given N_A=6×10²³)

Solution

Physics sir · 3 steps

First count the nuclei in 120 g, then multiply by the 200 MeV each one gives.

1. Moles of X. The molar mass of ²⁴⁰X is 240 g mol⁻¹. So 120 g is 120/240 = 0.5 mol.
2. Number of nuclei. Each mole has N_A atoms, so N = 0.5 × 6 × 10²³ = 3 × 10²³ nuclei.

   E = N × 200 MeV = 3 × 10²³ × 200 MeV = 6 × 10²⁵ MeV

3. So. The energy released is 6 × 10²⁵ MeV, so the blank is 6.

The common slip: 12. Treating the whole sample as one mole, with 6 × 10²³ nuclei, gives 12, not 6. 120 g of a 240 g/mol substance is only half a mole.

The idea to keep. Total fission energy is energy per fission times the number of nuclei. Get that number from mass divided by molar mass, times N_A.

Answer from the NTA final answer key. Solution by PrepWiser.