Physics Q29 – JEE-MAIN 2026

Two nuclei of mass number 3 combine with another nucleus of mass number 4 to yield a nucleus of mass number 10. If the binding energy per nucleon for the mass numbers 3, 4 and 10 are 5.6 MeV, 7.4 MeV and 6.1 MeV, respectively, then in the process,

Δ M c^{2} =

_______ MeV.

Clue 1 of 3: Conceptual Principle

In a nuclear reaction, the change in mass energy ( $Δ M c^{2}$ ) is related to the change in total binding energy of the nuclei involved.

🧠 Full Solution Path

Step 1: Calculate Total Binding Energy of Reactants✦ Active

The reaction involves two nuclei of mass number 3 and one nucleus of mass number 4. We calculate the total binding energy for each reactant type and sum them up.

B E_{A=3} = 3 \times 5.6 MeV = 16.8 MeV

Total B E_{reactants} = (2 \times B E_{A=3}) + (1 \times B E_{A=4})

Total B E_{reactants} = (2 \times 16.8 MeV) + (4 \times 7.4 MeV)

Total B E_{reactants} = 33.6 MeV + 29.6 MeV = 63.2 MeV

Step 2: Calculate Total Binding Energy of Products○ Expand

The reaction yields one nucleus of mass number 10. We calculate its total binding energy.

B E_{products} = 10 \times 6.1 MeV = 61.0 MeV

Step 3: Calculate the Change in Mass Energy (

Δ M c^{2}

)○ Expand

The change in mass energy, $Δ M c^{2}$ , is given by the difference between the total binding energy of the reactants and the total binding energy of the products. A positive value indicates energy absorption.

Δ M c^{2} = B E_{reactants} - B E_{products}

Δ M c^{2} = 63.2 MeV - 61.0 MeV = 2.2 MeV

💡 Teacher's Secret Hint

Remember that a positive $Δ M c^{2}$ means the final mass is greater than the initial mass, implying energy is absorbed in the process.

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Physics Question 29 – JEE-MAIN 2026

Clue 1 of 3: Conceptual Principle

🧠 Full Solution Path