RG's E-Learning Centre · Book a free demo class · WhatsApp +91-9379416374

Mass defect and binding energy: Class 12 practice

Mass defect Δm = (Z mₚ + N mₙ) − M_nucleus. Read the method, follow the three worked examples, then try the six questions.

What you should know first

  • Atomic structure

The idea behind mass defect and binding energy

Mass defect Δm = (Z mₚ + N mₙ) − M_nucleus. Binding energy = Δm × 931.5 MeV/u. Binding energy per nucleon tells how stable a nucleus is.

Step-by-step method

  1. Add masses of protons and neutrons.
  2. Subtract the nuclear mass to get Δm (u).
  3. BE = Δm × 931.5 MeV; divide by A for per nucleon.

Worked example 1 (Basic)

Find the mass defect and binding energy of ²H (nuclear mass 2.01355 u; mₚ = 1.00728 u, mₙ = 1.00866 u).

  1. Z = 1, N = 1
  2. Δm = 2.016 − 2.01355 = 0.00239 u
  3. BE = 2.23 MeV
  4. Answer: Δm = 0.00239 u, BE = 2.23 MeV

Worked example 2 (Standard)

Find the mass defect and binding energy of ¹²C (nuclear mass 11.99671 u; mₚ = 1.00728 u, mₙ = 1.00866 u).

  1. Z = 6, N = 6
  2. Δm = 12.096 − 11.99671 = 0.09893 u
  3. BE = 92.15 MeV
  4. Answer: Δm = 0.09893 u, BE = 92.15 MeV

Worked example 3 (Challenge)

Find the binding energy per nucleon of ¹⁶O (nuclear mass 15.99052 u; mₚ = 1.00728 u, mₙ = 1.00866 u).

  1. Z = 8, N = 8
  2. Δm = 16.128 − 15.99052 = 0.13700 u
  3. BE = 127.62 MeV
  4. Per nucleon = 7.98 MeV
  5. Answer: 7.98 MeV

Common mistakes and misconceptions

  • Using atomic number for the neutron count
  • Forgetting the 931.5 factor

Practice questions

  1. (Basic) Find the mass defect and binding energy of ⁴He (nuclear mass 4.00151 u; mₚ = 1.00728 u, mₙ = 1.00866 u).
  2. (Basic) Find the mass defect and binding energy of ⁷Li (nuclear mass 7.01436 u; mₚ = 1.00728 u, mₙ = 1.00866 u).
  3. (Standard) Find the mass defect and binding energy of ¹⁶O (nuclear mass 15.99052 u; mₚ = 1.00728 u, mₙ = 1.00866 u).
  4. (Standard) Find the mass defect and binding energy of ⁵⁶Fe (nuclear mass 55.92067 u; mₚ = 1.00728 u, mₙ = 1.00866 u).
  5. (Challenge) Find the binding energy per nucleon of ²H (nuclear mass 2.01355 u; mₚ = 1.00728 u, mₙ = 1.00866 u).
  6. (Challenge) Find the binding energy per nucleon of ⁴He (nuclear mass 4.00151 u; mₚ = 1.00728 u, mₙ = 1.00866 u).

Answer key with full working

  • Q1: Z = 2, N = 2 → Δm = 4.032 − 4.00151 = 0.03037 u → BE = 28.29 MeV → Answer: Δm = 0.03037 u, BE = 28.29 MeV
  • Q2: Z = 3, N = 4 → Δm = 7.056 − 7.01436 = 0.04212 u → BE = 39.23 MeV → Answer: Δm = 0.04212 u, BE = 39.23 MeV
  • Q3: Z = 8, N = 8 → Δm = 16.128 − 15.99052 = 0.13700 u → BE = 127.62 MeV → Answer: Δm = 0.13700 u, BE = 127.62 MeV
  • Q4: Z = 26, N = 30 → Δm = 56.449 − 55.92067 = 0.52841 u → BE = 492.21 MeV → Answer: Δm = 0.52841 u, BE = 492.21 MeV
  • Q5: Z = 1, N = 1 → Δm = 2.016 − 2.01355 = 0.00239 u → BE = 2.23 MeV → Per nucleon = 1.11 MeV → Answer: 1.11 MeV
  • Q6: Z = 2, N = 2 → Δm = 4.032 − 4.00151 = 0.03037 u → BE = 28.29 MeV → Per nucleon = 7.07 MeV → Answer: 7.07 MeV

Syllabus note

This skill is listed under "Nuclei" for Class 12 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.

Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.

Related practice and notes

Frequently asked questions

Which chapter is mass defect and binding energy in?

"Nuclei", Class 12 Physics (NCERT/CBSE). Other boards may place it differently.

How were the answers checked?

Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.

Book a free demo class