Problem 1 - A Complete Resource Book in Chemistry for JEE Main

Question

What is A in the following reaction? \({ }_{12} \mathrm{Mg}^{26}+{ }_{1} \mathrm{H}^{2} \longrightarrow{ }_{12} \mathrm{Mg}^{27}+\mathrm{A}\) (a) \({ }_{1} \mathrm{H}^{1}\) (b) \({ }_{0} \mathrm{n}^{1}\) (c) \({ }_{1} \mathrm{D}^{2}\) (d) \(\gamma\) rays

Step-by-Step Solution

Answer

A is 1H1 (option a).

Step 1: Understand the Reaction

This is a nuclear reaction involving magnesium (26), a hydrogen isotope (2), forming magnesium (27), and an unknown particle A. We need to identify A.

Step 2: Analyze the Reaction Equation

The reaction is given by 26 + 2 12 27 + A. Let's evaluate the components: the reactants and products must have the same total number of protons and neutrons.

Step 3: Calculate Total Atomic Numbers

For the reactants, we have: 12 (Mg) + 1 (H) = 13. For the products, 12 (Mg). For them to balance, A must have an atomic number of 1 (since 13 - 12 = 1).

Step 4: Calculate Total Mass Numbers

For the reactants, we have: 26 (Mg) + 2 (H) = 28. For the products, 27 (Mg). To balance the mass number, A must have a mass number of 1 (since 28 - 27 = 1).

Step 5: Identify the Unknown Particle A

From the calculated atomic and mass numbers for A (both 1), it matches with the hydrogen isotope 1, which is one proton.

Key Concepts

Isotope Calculations

Isotope calculations are essential when analyzing nuclear reactions because they allow us to track changes in nuclei during such reactions. Isotopes are variations of an element that have the same number of protons but different numbers of neutrons. This affects their atomic mass but not their chemical behavior.

In this exercise, we deal with isotopes of magnesium (\(^{26}\text{Mg}\)) and hydrogen (\(^{2}\text{H}\)). When performing isotope calculations, we focus on:

• Identifying the isotopes involved.
• Calculating the mass number (sum of protons and neutrons).
• Tracking how these numbers change before and after the reaction.

These calculations help determine unknown particles, like the particle A, by balancing the atomic and mass numbers on both sides of the equation.

Atomic Number Balance

The atomic number balance in nuclear reactions ensures that the number of protons—represented by the atomic number—remains consistent before and after the reaction. This is fundamental since it determines the identity of the element.

In the given reaction:- The atomic numbers of the reactants are 12 for \(^{26}\text{Mg}\) and 1 for \(^{2}\text{H}\), totaling 13.- On the product side, \(^{27}\text{Mg}\) has an atomic number of 12. To maintain balance, A must have an atomic number that satisfies 13 (reactants) = 12 (products) + 1 (A). Thus, A needs an atomic number of 1, hinting it could be a proton (\(^{1}\text{H}\)). This approach helps in predicting what missing particles or isotopes might be formed as a result of the reaction.

Mass Number Balance

Mass number balance requires that the total mass numbers of reactants equals the total mass numbers of products in nuclear reactions. Here's how this works:

- Reactants: The mass numbers add up to 28 (26 from \(^{26}\text{Mg}\) and 2 from \(^{2}\text{H}\)).- Products: \(^{27}\text{Mg}\) has a mass number of 27.For the mass number to remain equal, A must contribute a value that satisfies 28 (reactants) = 27 (products) + 1 (A). Consequently, the mass number of A must be 1, confirming that it is a single proton, consistent with the atomic number analysis.

This balance helps ensure that no naturally occurring physical laws are violated during the nuclear transformation, making it a crucial step in solving these types of exercises.