Problem 28 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

Assertion : Nuclide \(\frac{30}{13} \mathrm{Al}\) is less stable than \({ }_{20}^{40} \mathrm{Ca}\) Reason : Nuclides having odd number of protons and neutrons are generally unstable. (a) If both assertion and reason are correct, and reason is the correct explanation of the assertion. (b) If both assertion and reason are correct, but reason is not the correct explanation of the assertion. (c) If assertion is correct but reason is incorrect. (d) If assertion is incorrect but reason is correct.

Step-by-Step Solution

Answer

(a) Both assertion and reason are correct, and reason is the correct explanation of the assertion.

Step 1: Understanding the Assertion

The assertion claims that the nuclide \( \frac{30}{13} \mathrm{Al} \) is less stable than \( {}_{20}^{40} \mathrm{Ca} \). For a comparison of stability, look at the neutron-to-proton ratio, shell closure, and whether both have an even or odd number of protons and neutrons. \( {}_{20}^{40} \mathrm{Ca} \), a doubly magic nucleus with closed shells, is known to be stable.

Step 2: Evaluating Protons and Neutrons

For \( {}_{20}^{40} \mathrm{Ca} \), the numbers are even: 20 protons and 20 neutrons. For \( \frac{30}{13} \mathrm{Al} \), there are 13 protons and 17 neutrons, both of which are odd.

Step 3: Understanding the Reason

The reason states that nuclides with odd numbers of protons and neutrons are typically unstable. This is a correct general statement because stability is often higher in nuclides with even numbers of protons and neutrons.

Step 4: Evaluate Relationship Between Assertion and Reason

Given the reason, \( \frac{30}{13} \mathrm{Al} \) has odd protons and neutrons which contributes to its instability compared to \( {}_{20}^{40} \mathrm{Ca} \). The reason provided accurately explains why the assertion is true.

Key Concepts

Nuclide

A nuclide is a term used in nuclear chemistry and physics to describe a specific atomic species. Each nuclide is characterized by its number of protons and neutrons, which together make up an atom's nucleus. The identity of a nuclide is usually represented by its chemical symbol, atomic number, and mass number.
For example, the nuclide \( \frac{30}{13} \mathrm{Al} \) has the symbol Al for aluminum, an atomic number of 13 (indicating 13 protons), and a mass number of 30, accounting for both protons and neutrons.
Similarly, \({}_{20}^{40} \mathrm{Ca}\) indicates calcium with 20 protons and 40 as the mass number. This instantly tells us there are 20 neutrons, as the difference between the mass number and atomic number (40 - 20). Understanding nuclides helps in studying nuclear reactions and stability of different elements.

Protons and Neutrons

Protons and neutrons are fundamental particles that exist in an atom's nucleus. Together, they are known as nucleons. Protons carry a positive charge, while neutrons are neutral, having no charge.
The balance and quantity of protons and neutrons determine the element's identity as well as its isotopic form.

• Protons contribute to the atomic number, which defines the element.
• Neutrons, along with protons, are crucial in determining the stability of a nuclide.

The arrangement of protons and neutrons affects a nuclide's stability. Typically, nuclides with even numbers of both are more stable than those with odd numbers.
For example, \( {}_{20}^{40} \mathrm{Ca} \) has 20 protons and 20 neutrons, both even numbers, contributing to its stability. On the other hand, \( \frac{30}{13} \mathrm{Al} \), having 13 protons and 17 neutrons (both odd), is characteristically less stable.

Magic Numbers

In nuclear physics, magic numbers refer to numbers of nucleons (either protons or neutrons) that result in completed nuclear energy levels within an atomic nucleus.
Nuclides possessing magic numbers of protons or neutrons are extra stable and less likely to undergo radioactive decay.

• Common magic numbers include 2, 8, 20, 28, 50, 82, and 126.
• When both protons and neutrons are magic numbers, the nucleus is referred to as doubly magic, leading to exceptional stability.

The nuclide \({}_{20}^{40} \mathrm{Ca}\) is considered a doubly magic nucleus, with both protons and neutrons fitting a magic number (20 each), resulting in significant stability.
Understanding magic numbers helps explain why certain nuclides are inherently more stable, such as \({}_{20}^{40} \mathrm{Ca}\), compared to others like \(\frac{30}{13} \mathrm{Al}\), which does not fit into this magic number scheme and therefore exhibits less nuclear stability.