Q4. How long could a 100 W lamp glow on the energy from fusing 2.0 kg of deuterium by 2H + 2H → 3He + n + 3.27 MeV? (NCERT Exercise 13.8)
Nuclei = (2000/2.014) × 6.023 × 1023 ≈ 5.98 × 1026, so 2.99 × 1026 reactions. Energy ≈ 2.99 × 1026 × 3.27 × 1.6 × 10−13 J ≈ 1.565 × 1014 J. Assuming complete fuel use and 100% conversion to the lamp’s electrical energy, time = 1.565 × 1014/100 ≈ 1.565 × 1012 s ≈ 4.96 × 104 years (NCERT Exercise 13.8, page 322; NCERT’s answer on page 352 is about 4.9 × 104 years).
Q5. What is the average kinetic energy of a proton at the sun’s core temperature, 1.5 × 107 K? Compare it with the 400 keV barrier.
(3/2)kT = 1.5 × 1.381 × 10−23 × 1.5 × 107 ≈ 3.1 × 10−16 J ≈ 1.9 keV, about 200 times less than 400 keV. So fusion in the sun involves protons whose energies are much above the average (NCERT page 316). Beyond the NCERT text: they get through the barrier by quantum tunnelling, which allows fusion below the classical estimate (Wikipedia, “Proton–proton chain”).
Q6. Fission of one uranium-235 nucleus releases about 200 MeV. Burning carbon, C + O2 → CO2, releases 393.5 kJ mol−1 (NCERT Class 11 Chemistry, page 151). Compare the energy per fission with the energy per carbon atom burnt.
Per carbon atom: 393.5 × 103/(6.023 × 1023) ≈ 6.53 × 10−19 J ≈ 4.08 eV. Ratio = 200 × 106 eV/4.08 eV ≈ 4.9 × 107: MeV against eV (200 MeV from NCERT page 315; reasoned).
Q7. Why must the fuel in a fusion reactor be a plasma, and why is containing it hard?
At about 108 K the atoms are stripped into positive ions and electrons, a plasma, and no material container can stand such a temperature (NCERT page 317).
Q8. A nucleus with A = 200 and a binding energy of 7.9 MeV per nucleon splits into two nuclei with A = 100 and 8.6 MeV per nucleon. Estimate the energy released.
(8.6 − 7.9) MeV per nucleon × 200 nucleons ≈ 140 MeV: the products are more tightly bound (reasoned as in NCERT’s estimate, page 315).
Q9. The binding energies per nucleon of deuterium and helium-4 are about 1.1 MeV and 7.1 MeV. Estimate the energy released when two deuterons form helium-4 plus a gamma photon and recoil in the radiative branch.
After: 4 × 7.1 = 28.4 MeV; before: 2 × 2 × 1.1 = 4.4 MeV. Energy released ≈ 24 MeV (beyond the NCERT text; the masses in NCERT Exercise 13.5 give 23.8 MeV).
Q10. A reactor releases 100 MW of thermal power from fission of uranium-235, about 200 MeV per fission. How many fissions take place each second?
Energy per fission = 200 × 1.6 × 10−13 J = 3.2 × 10−11 J, so 108/(3.2 × 10−11) ≈ 3.1 × 1018 fissions per second (200 MeV from NCERT page 315).