Assertion (A): In sodium nucleus \(_{11}^{23}\text{Na}\), there are no electrons.
Reason (R): Atomic number of sodium is 11.
Nuclei contain protons and neutrons, not electrons. So (A) is true. Sodium's atomic number is 11. So (R) is true. (R) defines the element and proton count, but doesn't explain why electrons are outside the nucleus. So (R) does not explain (A).
Assertion (A): Atoms of greater mass number are more stable.
Reason (R): Their mass defects are more.
Nuclear stability depends on binding energy per nucleon, which peaks around \(A=56\). Very heavy nuclei are often unstable. So (A) is false. Total mass defect generally increases with mass number. So (R) is true.
Since (A) is false, options stating (A) is true are incorrect. With no 'A is false, R is true' option, (4) is selected due to question option constraints.
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.
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.
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): When a beam of highly energetic neutrons is incident on a tungsten target, X-rays will be produced.
Reason (R): Neutrons do not exert any electrostatic force on electrons or nucleus of an atom.
Assertion (A) can be true as energetic neutrons can cause nuclear reactions which might lead to secondary electrons or photons that produce X-rays. Reason (R) is also true as neutrons are electrically neutral.
However, the reason (R) explains why neutrons do not directly cause X-rays via electromagnetic interaction, not why they do produce X-rays (which would be an indirect process). Thus (R) is not the correct explanation for (A).
Assertion (A): Strong nuclear force holds protons inside nucleus.
Reason (R): Strong nuclear force is not a fundamental force.
Assertion (A) is true because the strong nuclear force binds nucleons (protons and neutrons) in the nucleus, overcoming electrostatic repulsion. Reason (R) is false as the strong nuclear force is one of the four fundamental forces of nature.
Assertion (A): Consider the following nuclear reaction of an unstable \(_6^{14}C\) nucleus initially at rest. The decay \(_6^{14}C to _7^{14}N + _{-1}^0e + \bar{nu}\). In a nuclear reaction total energy and momentum is conserved experiments show that the electrons are emitted with a continuous range of kinetic energies upto some maximum value.
Reason (R): Remaining energy is released as thermal energy.
Assertion (A) is true. In (beta) decay, the energy is shared between the electron and the antineutrino, leading to a continuous energy spectrum for the electron. Reason (R) is false. The continuous energy spectrum is due to the sharing of energy with the antineutrino, not conversion to thermal energy.
Assertion (A): The Q value of nuclear process is Q = total final binding energy – total initial binding energy.
Reason (R): The Q value of nuclear reaction initially appears in form of kinetic energy of products.
Assertion (A) is true by definition of Q-value: \(Q = sum BE_{products} - sum BE_{reactants}\). Reason (R) is also true, as the Q-value manifests as kinetic energy of products in exothermic reactions. However, (R) describes the consequence of Q-value, not its definition, so it's not the correct explanation for (A).
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.
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): \( \text{Fe}^{56} \) nucleus is more stable than \( \text{U}^{235} \) nucleus.
Reason (R): Binding energy of \( \text{Fe}^{56} \) nucleus is more than binding energy of \( \text{U}^{235} \).
\( \text{Fe}^{56} \) 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.