Animated Solution for Physics - Atoms and Nuclei: Consider the reaction : ${}_1^2\text{H}+{}_1^2\text{H}={}_2^4\text{He}+Q$. Mass of the deuterium atom = 2.0141 u. Mass of helium atom = 4.0024 u. This is a nuclear ........ reaction in which the energy $Q$ released is ...... MeV.

The energy that powers the stars, including our own Sun, comes from a process called nuclear fusion. In this thrilling problem, we get to calculate exactly how much energy is released when two light nuclei fuse together!

We are given a nuclear reaction where two deuterium nuclei (${}_1^2\text{H}$) combine to form a single helium nucleus (${}_2^4\text{He}$).

Whenever lighter nuclei combine to form a heavier, more stable nucleus, the process is known as nuclear fusion. This immediately gives us the answer to the first blank! But where does the released energy, $Q$, come from?

Mass Defect

According to Einstein's famous mass-energy equivalence principle, $E=m{c}^2$, mass and energy are interchangeable. In a fusion reaction, the total mass of the products is slightly less than the total mass of the reactants. This "missing mass" is called the mass defect ($\Delta m$), and it is converted entirely into energy!

The formula for mass defect is:

For our specific reaction:

Let's plug in the values given in the problem. The mass of one deuterium atom is $2.0141\text{ u}$, and the mass of the helium atom is $4.0024\text{ u}$.

Now, we perform the arithmetic carefully:

This $0.0258\text{ u}$ is the exact amount of mass that vanished during the reaction. To find the energy released, we use the standard conversion factor: $1\text{ u}$ of mass is equivalent to $931.4\text{ MeV}$ of energy.

The energy released is approximately $24\text{ MeV}$. This is a tremendous amount of energy for a single atomic event, which is why nuclear fusion holds such incredible promise as a future energy source for humanity!