QUESTION:
What is the energy released in the nuclear fusion reaction \rm _1^2H+_1^2H \rightarrow \ _2^4He + Q?
SOLUTION:
Given:
- A nuclear reaction; \rm _1^2H+_1^2H \rightarrow \ _2^4He + Q
To find:
- The energy released in the given fusion reaction.
We know the values:
- The unified atomic mass, \rm u = 931.5 \ MeV/c^2
- Mass of \rm _2^2H = 2.014102 \ u
- The mass of \rm _2^4He = 4.002602 \ u
The mass defect \Delta m of the given nuclear reaction is calculated as
\begin{aligned}\Delta m &= 2\times \text{Mass}(\rm _1^2H) – \text{Mass}(_2^4He )\\&= 2\times (2.014102\rm \ u) -(4.002602\rm \ u)\\&= 0.025602\rm \ u\\ &= 0.025602 \times 931.5\rm \ MeV/c^2\\ &=23.848263\rm \ MeV/c^2\\\end{aligned}
Therefore, the energy released in fusion reaction \rm _1^2H+_1^2H \rightarrow \ _2^4He is calculated as
\begin{aligned}E &= \Delta m c^2\\&=(23.848263\rm \ MeV/c^2) \times c^2\\&=23.848263\rm \ MeV\\\end{aligned}
Similar Problems based on Mass-Energy Equivalence
The isotope \rm ^{218}Po decays via \alpha-decay. The measured atomic mass of \rm ^{218}Po is 218.00897\rm \ u, and the atomic mass of the daughter nucleus is 213.99981\rm \ u. Find 1) the Name of the daughter nucleus, 2) the number of nucleons in the daughter nucleus, 3) the atomic number of the daughter nucleus, 4) the number of neutrons in the daughter nucleus, and 5) the kinetic energy of the \alpha-particle. (Ignore the recoil of the daughter nucleus.)
A free neutron can decay into a proton, an electron, and an anti-neutrino. Assume the anti-neutrino’s rest mass is zero, and the rest masses for proton and electron are 1.6726 \times 10^{ -27}\rm \ kg and 9.11\times10^{ -31}\rm \ kg respectively. Determine the total kinetic energy shared among the three particles when a neutron decays at rest.
The unified atomic mass unit, denoted by u, is defined to be \rm 1 u = 1.6605 \times 10^{ -27} \ kg. It can be used as an approximation for the average mass of a nucleon in a nucleus, taking the binding energy into account. Find the energy obtained after converting a nucleus of 14 nucleons completely into free energy.