Question

The energy released if hydrogen atoms are combined to form \(^{4}_{2}\text{He}\) is _____ MeV. (Take binding energies per nucleon of \(^{2}_{1}\text{H}\) and \(^{4}_{2}\text{He}\) as \(1.1\,\text{MeV}\) and \(7.2\,\text{MeV}\), respectively).

• A. \(6.1\)
• B. \(24.4\)
• C. \(26.6\)
• D. \(5\)

Answer 1

The Correct Option is B

Concept: Energy released in nuclear fusion equals increase in binding energy. \[ \text{Binding energy} = (\text{binding energy per nucleon}) \times (\text{number of nucleons}) \] Step 1: {Find initial binding energy.} Four hydrogen nuclei form two deuterium nuclei first. Binding energy per nucleon of \(^{2}_{1}\text{H}\): \[ 1.1\,\text{MeV} \] Total nucleons: \[ 4 \] Thus initial binding energy: \[ 4\times1.1=4.4\,\text{MeV} \] Step 2: {Find final binding energy.} For \(^{4}_{2}\text{He}\): \[ 7.2\,\text{MeV per nucleon} \] Total binding energy: \[ 4\times7.2=28.8\,\text{MeV} \] Step 3: {Energy released.} \[ E=28.8-4.4 \] \[ =24.4\,\text{MeV} \]