Problem 119 - A Complete Resource Book in Chemistry for JEE Main

Question

Select the correct statements: (a) In the reaction \({ }_{11} \mathrm{Na}^{23}+\mathrm{Q} \rightarrow{ }_{12} \mathrm{Mg}^{23}+{ }_{0} \mathrm{n}^{1}\), the bombarding particle \(\mathrm{q}\) is deutron (b) In the reaction \({ }_{92} \mathrm{U}^{235}+{ }_{0} \mathrm{n}^{1} \rightarrow 56 \mathrm{Ba}^{140}+2\) \({ }_{0} \mathrm{n}^{1}+\mathrm{p}\), produced \(\mathrm{p}\) is \({ }_{36} \mathrm{Kr}^{94}\) (c) In a fission reaction, a loss in mass occurs releasing a huge amount of energy (d) A huge amount of energy is produced during nuclear fission and nuclear fussion reaction

Step-by-Step Solution

Answer

Statements (a), (c), and (d) are correct; (b) needs clarification but seems correct.

Step 1: Analyze Statement (a)

The nuclear reaction given is \( _{11} \text{Na}^{23} + Q \rightarrow _{12} \text{Mg}^{23} + _{0} \text{n}^{1} \). We need to determine the identity of \( Q \). The atomic number (lower left number) of sodium is 11, and magnesium is 12. This means the added particle \( Q \) must have an atomic number of 1 (proton) to increase the atomic number by one. Also, the mass number should remain 23, meaning \( Q \) must have a mass number of 2. The only particle with these characteristics is a deutron \((^2_1\text{H})\). Thus, statement (a) is correct.

Step 2: Analyze Statement (b)

The reaction \( _{92} \text{U}^{235} + _{0} \text{n}^{1} \rightarrow _{56} \text{Ba}^{140} + 2 \, _{0} \text{n}^{1} + p\) is presented, where the produced particle \( p \) is stated as \( _{36} \text{Kr}^{94} \). Calculate the expected products:- Original mass number: 235 (Uranium) + 1 (neutron) = 236- Mass number of products given: 140 (Barium) + 94 (Kr) + 2 neutrons = 236.- Atomic numbers: 92 (U) becomes 56 (Ba) + 36 (Kr) = 92.The atomic and mass numbers balance, suggesting the reaction and product \( _{36} \text{Kr}^{94} \) are correctly stated unless there's a typographical note missed. We conclude the statement is potentially accurate but should be confirmed with source details.

Step 3: Analyze Statement (c)

Statement (c) suggests a mass loss in fission reactions resulting in energy release. According to Einstein’s mass-energy equivalence principle \( E=mc^2 \), the loss of mass (\( \Delta m \)) is converted to energy. This statement corresponds to the conceptual understanding of nuclear fission, making (c) a correct statement.

Step 4: Analyze Statement (d)

Statement (d) suggests that a huge amount of energy is produced in both nuclear fission and fusion reactions. Both processes involve the conversion of mass to energy via Einstein's \( E=mc^2 \). Thus, energy is indeed released significantly in both processes, making statement (d) correct.

Key Concepts

Nuclear Fission

Nuclear fission is a fascinating process that occurs when the nucleus of a heavy atom, such as uranium-235, splits into two or more smaller nuclei. This splitting is often triggered by the absorption of a neutron, leading to the release of a substantial amount of energy, additional neutrons, and other smaller atomic nuclei.
The additional neutrons can go on to trigger more fission events, creating a chain reaction that releases even more energy.
Fission is the principle behind nuclear reactors and atomic bombs, where controlled fission reactions provide a steady source of energy.

• In the context of energy, fission reactions release a massive amount of energy due to the conversion of a small amount of mass into energy.
• The principle of mass-energy equivalence, represented by Einstein's famous equation \( E=mc^2 \), explains how mass is converted into energy during the process.

Nuclear Fusion

Nuclear fusion, often described as the power of the stars, is the process by which two light atomic nuclei combine to form a heavier nucleus. This process is accompanied by the release of energy.
Fusion is responsible for the energy produced by the sun and other stars as hydrogen nuclei combine under extreme pressure and temperature to form helium and release energy.

• Unlike fission, which splits heavy elements, fusion joins lighter elements.
• It is a cleaner source of energy and produces fewer radioactive byproducts than fission but requires extremely high temperatures.

The potential of fusion as a future energy source is immense due to its sustainable and virtually limitless fuel supply, primarily hydrogen isotopes like deuterium and tritium.

Mass-Energy Equivalence

The concept of mass-energy equivalence is central to understanding nuclear reactions. This principle is encapsulated in Einstein’s equation \( E=mc^2 \), which states that energy \( E \) is equal to mass \( m \) multiplied by the speed of light \( c \) squared.
In nuclear reactions, a small amount of mass can be converted into a significant amount of energy.

• This conversion fuels the power of atomic bombs and nuclear reactors through fission.
• It also explains the energy output of stars and proposed fusion energy systems.

Mass-energy equivalence helps explain how energy is conserved even when mass seems to vanish in nuclear transformations, thus giving insights into the true nature of energy release in nuclear processes.

Deuteron

A deuteron is the nucleus of deuterium, an isotope of hydrogen, consisting of one proton and one neutron, giving it the atomic notation \(^2_1\text{H}\).
Deuterons are crucial in nuclear fusion processes, particularly those involving the fusion of deuterium nuclei into helium, releasing significant energy.

• In nuclear reactions, deuterons can act as projectiles to initiate permissible reactions, such as converting one element into another.
• They are used in experimental fusion reactors, which aim to harness fusion power for electricity generation.

Thanks to its dual nature—a combination of proton and neutron—deuteron plays a highly versatile role in the study of nuclear physics and potential energy resources.