Animated Solution for Physics - Atoms and Nuclei: Match Column I of the nuclear process with Column II containing parent nucleus and one of the end products of each process and then select the correct answer using the codes given below the lists.

A Matrix Match Challenge

Welcome to a fascinating journey into the heart of the atom! In this classic matrix match problem from Modern Physics, we are tasked with identifying the specific nuclear processes occurring in four distinct reactions. The key to unlocking this puzzle lies in the fundamental laws of conservation: the conservation of mass number ($A$) and atomic number ($Z$). Let's break down each process and find its perfect match.

We are given four nuclear processes in Column I: Alpha decay, ${\beta }^{+}$ decay, Fission, and Proton emission. In Column II, we have four incomplete nuclear reactions. Our goal is to analyze the changes in the mass number (the superscript) and the atomic number (the subscript) from the parent nucleus to the daughter nucleus to deduce which particle was emitted.

Let's start with Alpha decay. An alpha particle is essentially a Helium nucleus, consisting of two protons and two neutrons. Its symbol is ${}_2^4\text{He}$ or ${}_2^4\alpha$.

When a nucleus undergoes alpha decay, it ejects this heavy particle. Consequently, its mass number ($A$) must decrease by exactly 4, and its atomic number ($Z$) must decrease by exactly 2.

Now, let's scan the reactions in Column II. Look closely at reaction 2:

The mass number goes from 238 to 234, a drop of 4. The atomic number goes from 92 to 90, a drop of 2. This perfectly matches the signature of alpha decay! Therefore, P matches with 2.

Next, we explore ${\beta }^{+}$ decay, also known as positron emission. In this intriguing process, a proton inside the nucleus transforms into a neutron, emitting a positron (${}_{+1}^0\beta$) and a neutrino.

Because a proton becomes a neutron, the total number of nucleons (protons + neutrons) remains unchanged. Thus, the mass number ($A$) is constant. However, since we lost a proton, the atomic number ($Z$) decreases by 1.

Let's check reaction 1:

The mass number is constant at 15, but the atomic number drops from 8 to 7. This is a clear case of ${\beta }^{+}$ decay. Therefore, Q matches with 1.

Moving on to Nuclear Fission. This is a dramatic process where a heavy, unstable nucleus splits into two or more lighter nuclei of comparable masses, often releasing neutrons and a massive amount of energy.

Look at reaction 4:

Plutonium-239, a very heavy nucleus, is breaking apart to form Lanthanum-140, a much lighter nucleus, along with other fragments. This massive splitting is the hallmark of nuclear fission. Therefore, R matches with 4.

Finally, we have Proton emission. As the name suggests, the nucleus simply ejects a proton (${}_1^{1}p$).

A proton has a mass number of 1 and an atomic number of 1. So, both the mass number and the atomic number of the parent nucleus must decrease by exactly 1.

Observe reaction 3:

The mass number drops from 185 to 184, and the atomic number drops from 83 to 82. This is exactly what happens in proton emission. Therefore, S matches with 3.

By meticulously applying the conservation laws, we have successfully decoded all the nuclear processes. The final matching is: - P $\to$ 2 - Q $\to$ 1 - R $\to$ 4 - S $\to$ 3

Mastering these patterns is like learning to balance chemical equations, but for the very core of matter itself!