Question

A certain mass of Hydrogen is changed to Helium by the process of fusion. The mass defect in fusion reaction is 0.02866 u. The energy liberated per u is (given 1 u=931 MeV)

• A. 2.67 MeV
• B. 26.7 MeV
• C. 6.675 MeV
• D. 13.35 MeV

Answer 1

The Correct Option is C

 First, let's understand the problem: We are given a process of fusion where Hydrogen is converted to Helium, and there's a mass defect of \(0.02866 \, \text{u}\) in the reaction.

The energy equivalent of a mass defect can be calculated using Einstein’s mass-energy equivalence relation:

\(E = \Delta m \cdot c^2\)

Where:

• \(\Delta m\) is the mass defect.
• \(c\) is the speed of light, but in nuclear physics calculations, this is typically expressed in terms of energy equivalent of mass defect: \(1 \, \text{u} = 931 \, \text{MeV}\).

Given that the mass defect \(\Delta m = 0.02866 \, \text{u}\), the energy liberated from this mass defect would be:

\(E = 0.02866 \, \text{u} \times 931 \, \text{MeV/u}\)

Performing the calculation:

\(E = 0.02866 \times 931 = 26.67506 \, \text{MeV}\)

Now, we are asked to find the energy liberated per atomic mass unit (\(\text{u}\)). Given the energy liberated calculated above, we'll divide it by the 4 \(u\) since energy per nucleon is typically considered with respect to the number of nucleons (Helium nucleus):

\(E_{\text{per u}} = \frac{26.67506 \, \text{MeV}}{4} = 6.668765 \, \text{MeV}\)

This value approximates to 6.675 MeV, matching the option

6.675 MeV

1. .

 

Hence, the energy liberated per \(\text{u}\) is 6.675 MeV, which is the correct answer.