The atomic mass of ₆ C¹² is 12.000000 u and that of ₆ C¹³ is 13.003354 u. The required energy to remove a neutron from ₆ C¹³, if mass of neutron is 1.008665 u, will be :

Solution

Physics sir · 4 steps

Pull the neutron out and weigh both sides: the missing mass is the energy you must supply.

1. Set up the reaction. Removing a neutron means ¹³₆C → ¹²₆C + ¹₀n. The products together weigh more than ¹³₆C, so energy has to be put in to make this happen.

   Δ m = (m_(¹²C) + mₙ) - m_(¹³C)

2. Find the mass difference. Products: 12.000000 + 1.008665 = 13.008665 u. Subtract 13.003354 u to get Δ m = 0.005311 u.
3. Convert to energy. Use 1 u = 931.5 MeV: E = 0.005311 × 931.5 = 4.947 MeV.
4. So. The energy needed to remove the neutron is about 4.95 MeV, which is option (c).

The idea to keep. Separation energy of a particle = (mass of the pieces after removal) minus (mass of the original nucleus), times 931.5 MeV per u. Atomic masses work because the electrons cancel.

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