The energy released if hydrogen atoms are combined to form 42He is _______ MeV. (Take binding energies per nucleon of 21H and 42He as 1.1 MeV and 7.2 MeV, respectively)

The correct answer is Option 2. Full mathematical solution steps and hints are accessible in the interactive StemCET workspace.

Physics Q41 – JEE-MAIN 2026

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Home Physics NucleiQuestion #368

The energy released if hydrogen atoms are combined to form

_{2}^{4} He

is _______ MeV. (Take binding energies per nucleon of

_{1}^{2} H

and

_{2}^{4} He

as 1.1 MeV and 7.2 MeV, respectively)

Clue 1 of 3: Understand Nuclear Fusion

Energy is released when lighter nuclei combine to form a heavier, more stable nucleus. This energy release is related to the change in binding energy.

🧠 Full Solution Path

Step 1: Identify the Nuclear Reaction and Calculate Total Binding Energies of Reactants✦ Active

The fusion reaction to form $_{2}^{4} He$ from hydrogen atoms (specifically deuterium, $_{1}^{2} H$ , as its binding energy is provided) is:

2_{1}^{2} H \to_{2}^{4} He

The binding energy per nucleon for $_{1}^{2} H$ is $1.1 MeV$ . Therefore, the total binding energy of one $_{1}^{2} H$ nucleus is $2 \times 1.1 MeV = 2.2 MeV$ . The total binding energy of the reactants ( $2_{1}^{2} H$ ) is $2 \times 2.2 MeV = 4.4 MeV$ .

Step 2: Calculate Total Binding Energy of the Product○ Expand

The binding energy per nucleon for $_{2}^{4} He$ is $7.2 MeV$ . The total binding energy of one $_{2}^{4} He$ nucleus is $4 \times 7.2 MeV = 28.8 MeV$ .

Step 3: Calculate the Energy Released○ Expand

The energy released (Q-value) in a nuclear reaction is the difference between the total binding energy of the products and the total binding energy of the reactants:

Energy released = B E (products) - B E (reactants)

Substituting the calculated values:

Energy released = B E (_{2}^{4} He) - 2 \times B E (_{1}^{2} H)

Energy released = 28.8 MeV - 4.4 MeV = 24.4 MeV

💡 Teacher's Secret Hint

Ensure you subtract the total binding energy of all reactant nuclei from the total binding energy of all product nuclei.

✦ STEM Console utilizes AI models to generate step-by-step explanations and math clues. AI can make mistakes.

Physics Question 41 – JEE-MAIN 2026

Clue 1 of 3: Understand Nuclear Fusion

🧠 Full Solution Path