Problem 109 - A Complete Resource Book in Chemistry for JEE Main

Question

Match the following: List-I List-II (Reactions) (Particles) 1\. \({ }_{4} \mathrm{Be}^{9}+{ }_{2} \mathrm{He}^{4} \longrightarrow{ }_{6} \mathrm{C}^{12}+\ldots \ldots\) (i) \({ }_{2} \mathrm{He}^{4}\) 2\. \({ }_{6} \mathrm{C}^{12}+\ldots \ldots \longrightarrow{ }_{5} \mathrm{~B}^{10}+{ }_{2} \mathrm{He}^{4}\) (ii) \({ }_{0} \mathrm{n}^{1}\) \(3 .{ }_{7} \mathrm{~N}^{14}+\ldots \ldots \longrightarrow{ }_{8} \mathrm{O}^{17}+{ }_{1} \mathrm{H}^{1}\) (iii) \({ }_{1} \mathrm{D}^{2}\) 4\. \({ }_{20} \mathrm{Ca}^{40}+\ldots \ldots \longrightarrow{ }_{19} \mathrm{~K}^{37}+{ }_{2} \mathrm{He}^{4}\) (iv) \({ }_{1} \mathrm{H}^{1}\) The correct matching is: (a) (ii)(i) (iii) (iv) (b) (iii) (ii)(i) (iv) (c) (i) (ii) (iv) (iii) (d) (ii) (iii) (i) (iv)

Step-by-Step Solution

Answer

Option (c): (i)(ii)(iv)(iii) is correct.

Step 1: Solve Reaction 1

The reaction is \( _{4}\mathrm{Be}^{9} + _{2}\mathrm{He}^{4} \rightarrow _{6}\mathrm{C}^{12} + \ldots \) This equation involves the sum of atomic numbers and mass numbers on both sides. The atomic numbers are \(4 + 2 = 6\), so there is no missing charge. The mass numbers are \(9 + 4 = 13\), while the carbon atom is \(12\). Therefore, the missing particle must have a mass number of \(1\), which corresponds to \(_{1}\mathrm{H}^{1}\). Thus, the match is (iv).

Step 2: Solve Reaction 2

The reaction is \( _{6}\mathrm{C}^{12} + \ldots \rightarrow _{5}\mathrm{B}^{10} + _{2}\mathrm{He}^{4} \) Balancing the atomic numbers, we have \(6\) on the left and \(5 + 2 = 7\) on the right. Therefore, the missing particle has an atomic number of \( -1\), typically indicating a neutron \(_{0}\mathrm{n}^{1}\). This matches to (ii).

Step 3: Solve Reaction 3

The reaction is \( _{7}\mathrm{N}^{14} + \ldots \rightarrow _{8}\mathrm{O}^{17} + _{1}\mathrm{H}^{1} \) Balancing the atomic numbers, we have \(7\) on the left and \(8 + 1 = 9\) on the right. Thus, the missing particle must have an atomic number of \(2\), suggesting \(_{2}\mathrm{He}^{4}\) or \(\alpha\) particle. This matches to (i).

Step 4: Solve Reaction 4

The reaction is \( _{20}\mathrm{Ca}^{40} + \ldots \rightarrow _{19}\mathrm{K}^{37} + _{2}\mathrm{He}^{4} \) The atomic numbers sum to \(20\) on the left and \(19 + 2 = 21\) on the right. Therefore, the missing particle must have an atomic number of \(-1\), indicating a proton \(_{1}\mathrm{H}^{1}\). This matches to (iv).

Step 5: Match the Correct Options

After solving each reaction step-by-step, we arrive at the following matches:1. Reaction 1: (iv) \(_{1}\mathrm{H}^{1}\)2. Reaction 2: (ii) \(_{0}\mathrm{n}^{1}\)3. Reaction 3: (i) \(_{2}\mathrm{He}^{4}\)4. Reaction 4: (iii) \(_{1}\mathrm{H}^{1}\)This corresponds to option (c): (i) (ii) (iv) (iii).

Key Concepts

Atomic Number

The atomic number of an element is a fundamental concept in nuclear reactions and particle physics. It is the number of protons found in the nucleus of an atom. This number is unique to each element and defines the element's identity on the periodic table. For example, carbon always has an atomic number of 6, meaning every carbon atom has 6 protons.
In nuclear reactions, understanding the atomic number is crucial because it helps in balancing nuclear equations. When atoms undergo nuclear reactions, such as fusion or fission, they might absorb or release particles like protons (hydrogen nuclei), neutrons, or alpha particles (helium nuclei). The reactions must be balanced in terms of both atomic numbers and mass numbers.
For instance, in the reaction \[{ }_{4} \mathrm{Be}^{9} + { }_{2} \mathrm{He}^{4} \longrightarrow { }_{6} \mathrm{C}^{12} + \_ \_ \_ \] the sum of the atomic numbers on the left is 4 + 2 = 6, which equals the atomic number of carbon on the right side of the equation. If you were to solve for a missing particle, you'd need to ensure the total atomic numbers on both sides remain equal.

Mass Number

The mass number of an atom is another vital concept in understanding nuclear reactions. It represents the total number of protons and neutrons in an atom's nucleus. Unlike the atomic number, the mass number is not unique to each element since an element can have different isotopes. Isotopes are atoms of the same element with the same atomic number but different mass numbers due to varying numbers of neutrons.
When balancing nuclear equations, the mass number must also be conserved. This means the total mass number on the reactant side of the equation must equal the total mass number on the product side.
For example, in the reaction \[{ }_{4} \mathrm{Be}^{9} + { }_{2} \mathrm{He}^{4} \rightarrow { }_{6} \mathrm{C}^{12} + \_ \_ \_ \] the sum of mass numbers on the left is 9 + 4 = 13. The carbon product has a mass number of 12, so a missing particle must account for that extra 1 in mass number, indicating possibly a proton or other particle, depending on the reaction details.

Particle Physics

Particle physics is a branch of science that studies the characteristics and interactions of particles that are smaller than atoms, primarily the components of the atom's nucleus. The main particles involved include protons, neutrons, and electrons. In nuclear reactions, even smaller particles such as alpha particles, beta particles, and neutrinos may also be involved.
Understanding these particles and their roles in nuclear reactions is crucial. Protons and neutrons make up the nucleus, while electrons orbit the nucleus. In nuclear reactions, particles like alpha particles (\( _{2} \mathrm{He}^{4} \)) or neutrons (\( _{0} \mathrm{n}^{1} \)) can be emitted, absorbed, or rearranged, leading to the transformation of elements.
For instance, in the exercise, Particle (i) \( _{2} \mathrm{He}^{4} \) represents an alpha particle. This is a crucial component in certain types of nuclear reactions, altering both atomic and mass numbers as seen in transformations from one element to another or when certain nuclear reactions take place.

Balancing Equations

Balancing equations is an important process in both chemical and nuclear reactions to ensure that the law of conservation of mass and energy is observed. This means that the total mass and energy before and after the reaction must remain constant.
In nuclear equations, this involves ensuring that the sum of atomic numbers and mass numbers on the reactant side is equal to those on the product side.
To balance an equation:- Write down the known reactants and products.- Ensure the total atomic number on both sides of the equation is the same.- Similarly, match the total mass number on both sides.
For example:In the response step '3', the equation \( _{7} \mathrm{N}^{14} + \ldots \rightarrow _{8} \mathrm{O}^{17} + _{1} \mathrm{H}^{1} \) is balanced by ensuring the reactants and products have equal atomic and mass numbers, solving for the missing component, often with trial and error using the provided possible particle list.
This skill is not only crucial in academia but also in areas like nuclear engineering and physics, where precise knowledge of these principles is necessary for practical applications.