Assertion (A): The effective mass of (beta)-particles when they are emitted is higher than the mass of electrons obtained by Millikan oil-drop experiment.
Reason (R): (beta)-particle and electron, both are similar particles.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Assertion (A) is true. (beta)-particles are emitted with high speeds, so their relativistic mass \(m = m_0/\sqrt{1 - v^2/c^2}\) is higher than their rest mass \(m_0\). Reason (R) is also true, as (beta)-particles are electrons. However, (R) does not explain the relativistic mass increase in (A).
Assertion (A): If number of protons in a nucleus is more than number of neutrons present, the nucleus is unstable.
Reason (R): Electrostatic force between two protons in a nucleus dominates over the nuclear force between them.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Assertion (A) is true. Nuclei with a significant excess of protons over neutrons ((Z > N)) are generally unstable due to increased electrostatic repulsion. Reason (R) is false.
The strong nuclear force is much stronger than the electrostatic force between two protons at nuclear distances. Nuclear instability arises from the cumulative effect of long-range electrostatic repulsion overcoming the short-range strong nuclear attraction for a large number of protons.
Assertion (A): Nucleus having more binding energy is more stable.
Reason (R): Stability increases with increase in number of nucleons.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Assertion (A) is false. A nucleus with higher *total* binding energy is not necessarily more stable; stability is determined by binding energy *per nucleon*. For example, \(^{238}U\) has more total binding energy than \(^{56}Fe\) but is less stable. Reason (R) is also false. Nuclear stability increases with nucleon number up to (A approx 56) (Iron) and then decreases for heavier nuclei.
Assertion (A): Strong nuclear force is fundamental quark-quark interaction.
Reason (R): Strong nuclear force is shortest range force in nature.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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The strong nuclear force is a fundamental interaction between quarks, mediated by gluons. So (A) is true. It also has the shortest range among all fundamental forces. So (R) is true. However, the range of the force doesn't explain its fundamental nature as a quark interaction.
Assertion (A): The value of Rydberg constant is independent of mass of nucleus.
Reason (R): Electrons revolve around stationary nucleus of atom.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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The Rydberg constant for a given atom depends on the reduced mass, which includes the nuclear mass. So (A) is false. The assumption of a stationary nucleus is an approximation; both electron and nucleus orbit their center of mass. So (R) is false.
Assertion (A): Fragments produced in the fission of \( \text{_{92}^{235}U} \) are radioactive.
Reason (R): The fragments have abnormally high proton to neutron ratio.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Fission fragments are typically neutron-rich and undergo beta-minus decay to reach stability, thus being radioactive. So (A) is true. They have a high neutron-to-proton ratio (or low proton-to-neutron ratio), not a high proton-to-neutron ratio. So (R) is false.
Assertion (A): The binding energy per nucleon, for nuclei with atomic mass number \( A > 100 \) decreases with \( A \).
Reason (R): The nuclear forces become weaker for heavier nuclei.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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The binding energy per nucleon peaks around \( A=60 \) and decreases for heavier nuclei due to increasing Coulomb repulsion, which effectively weakens the average nuclear force per nucleon. Both (A) and (R) are true, and (R) correctly explains (A).
Assertion (A): All protons have non zero magnetic moment.
Reason (R): All nuclei have non zero magnetic moment.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Protons possess intrinsic spin and thus a non-zero magnetic moment. So (A) is true. Nuclei with even numbers of both protons and neutrons (even-even nuclei) have zero net spin and zero magnetic moment. So (R) is false.
Assertion (A): Rydberg constant varies with mass number of a given element.
Reason (R): The reduced mass of electron depends on the mass of the nucleus.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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The effective Rydberg constant for an atom depends on the reduced mass \( \mu = \frac{m_e M}{m_e + M} \), where \( M \) is the nuclear mass (related to mass number). So, (A) is true. The reduced mass clearly depends on the nuclear mass. So (R) is true. (R) correctly explains (A).
Assertion (A): \( \text{Fe}^{56} \) nucleus is more stable than \( \text{U}^{235} \) nucleus.
Reason (R): Binding energy of \( \text{Fe}^{56} \) nucleus is more than binding energy of \( \text{U}^{235} \).
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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\( \text{Fe}^{56} \) has the highest binding energy per nucleon, making it the most stable. So (A) is true. The total binding energy of \( \text{U}^{235} \) is much higher than \( \text{Fe}^{56} \) due to its larger number of nucleons. Thus (R) is false.