To find the energy released in this nuclear reaction, we use the concept of mass defect and Einstein's massenergy equivalence principle. The mass defect is the difference between the mass of the reactants and the mass of the products in a nuclear reaction. According to Einstein's relation,
E=mc2, where
E is the energy released,
m is the mass defect, and
c is the speed of light in vacuum.
Given data:
Mass of deuteron
=2.01355‌amuMass of helium nucleus
=4.0028‌amuThe reaction involves two deuteron nuclei combining into one helium nucleus. First, let's calculate the total mass of the reactants ( 2 deuterons):
Total mass of reactants
=2× mass of deuteron
=2×2.01355‌amuTotal mass of reactants
=4.0271‌amuNow, let's find the mass defect
(∆m), which is the difference between the mass of the reactants and the mass of the product (helium nucleus):
‌∆m=‌ Total mass of reactants ‌−‌ mass of product ‌
‌∆m=4.0271‌amu−4.0028‌amu‌∆m=0.0243‌amuTo convert the mass defect from atomic mass units (amu) to kilograms (kg), we use the conversion factor
‌1‌amu=1.660539040×10−27‌kg:‌∆m(kg)=0.0243‌amu×1.660539040×10−27‌kg∕amu
‌∆m(kg)=4.03311×10−29‌kg The energy released can now be calculated using the formula
E=mc2, where
c=2.99792458×108m∕ s (speed of light):
‌E=(4.03311×10−29‌kg)×(2.99792458×108m∕ s)2
‌E=3.62894×10−12JTo convert energy from Joules to Mega-electronvolts
(MeV. ), we use
1J=6.242×1012‌MeV :
‌E=3.62894×10−12J×6.242×1012‌MeV∕J
‌E=22.65‌MeVThe energy released is approximately
22.65‌MeV, which is closest to Option
C,22.62‌MeV. Therefore, Option
C is the correct answer.