Animated Solution for Physics - Atoms and Nuclei: Match the nuclear processes given in Column I with the appropriate option(s) in Column II.

From Stars to Reactors

Nuclear physics governs the fundamental processes that power our universe, from the core of the sun to the heart of a nuclear reactor. In this matrix match problem, we are tasked with connecting four distinct nuclear phenomena with their corresponding characteristics. Let's embark on a thrilling journey through these processes to uncover the correct matches.

Nuclear Fusion

When we look up at the night sky, the light we see is the result of Nuclear Fusion. In the extreme temperatures and pressures of a star's core, lighter nuclei overcome their immense electrostatic repulsion to fuse together. The most common sequence is the proton-proton chain, where hydrogen nuclei fuse to form helium:

This process releases a staggering amount of energy ($Q$) due to the mass defect, as dictated by Einstein's famous equation $E=m{c}^2$. Crucially, to conserve lepton number, this fusion process emits neutrinos ($ u$). Therefore, Nuclear Fusion (A) perfectly matches with energy production in stars (R) and neutrino emission (T).

Nuclear Fission

In stark contrast to fusion, Nuclear Fission involves the splitting of a heavy, unstable nucleus into lighter fragments. In a typical nuclear reactor, Uranium-235 (${}_{92}^{235}\text{U}$) is bombarded with neutrons. However, U-235 has a much higher capture cross-section for slow-moving, thermal neutrons.

When U-235 absorbs a thermal neutron, it becomes highly unstable and splits, releasing more fast neutrons. To sustain a controlled chain reaction, these fast neutrons must be slowed down. This is where a moderator comes into play. Heavy water ($D_{2}O$) is an excellent moderator because it slows down neutrons without absorbing them significantly. Thus, Fission in a nuclear reactor (B) matches with the absorption of thermal neutrons by U-235 (P) and the use of heavy water (S).

$\beta$-decay is a manifestation of the weak nuclear force, where a neutron transforms into a proton (or vice versa) within the nucleus. A classic example is the radioactive isotope Cobalt-60 (${}_{27}^{60}\text{Co}$), which undergoes ${\beta }^{-}$-decay to become Nickel-60:

Notice the emission of the antineutrino ($\bar{ u}$). Wolfgang Pauli originally postulated the existence of the neutrino to explain the continuous energy spectrum of the emitted beta particles, ensuring that energy and momentum are strictly conserved. Therefore, $\beta$-decay (C) matches with the Cobalt-60 nucleus (Q) and neutrino emission (T).

Following a $\beta$-decay, the daughter nucleus is often left in an excited, higher-energy state (denoted by the asterisk in ${}_{28}^{60}{\text{Ni}}^{\ast }$). Just as an excited electron drops to a lower energy level by emitting a photon, an excited nucleus relaxes to its ground state by emitting a high-energy photon known as a $\gamma$-ray.

Because Cobalt-60 decay reliably produces these high-energy gamma rays, it is widely used in medical radiotherapy and industrial radiography. Hence, $\gamma$-ray emission (D) matches directly with the Cobalt-60 nucleus (Q).

By meticulously analyzing the physics behind each process, we have successfully decoded the matrix:

A maps to R, T B maps to P, S C maps to Q, T D maps to Q

Understanding these connections not only solves the problem but also deepens our appreciation for the elegant and powerful laws governing the atomic nucleus.