Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Nucleus having more binding energy per nucleon is more stable.
Reason (R): Stability increase with increase in number of nucleons.
In the light of the above statements, choose the correct answer from the options given below.
1. Both (A) and (R) are true and (R) is the correct explanation of (A)
2. Both (A) and (R) are true but (R) is not the correct explanation of (A)
3. (A) is true but (R) is false
4. (A) is false but (R) is true
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Assertion is true because binding energy per nucleon is the direct measure of nuclear stability. Reason is false because stability does not simply increase with nucleon number; heavy nuclei with a very large number of nucleons become unstable.
Assertion (A): An electron and a positron moving towards each other with equal and opposite velocities can annihilate into photons.
Reason (R): A photon has non zero energy and momentum.
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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Electron-positron annihilation converts their mass-energy into radiant energy, typically two gamma-ray photons to conserve momentum. Photons indeed possess non-zero energy and momentum. However, the reason describes a property of the resulting photons rather than the fundamental cause or mechanism of the annihilation process itself.
Assertion (A): For the scattering of \(\alpha\)-particles at a large angles only the nucleus of the atom is responsible.
Reason (R): Nucleus is very heavy in comparison to electrons.
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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In Rutherford's alpha-scattering experiment, large-angle deflections are caused by the strong electrostatic repulsion from the positively charged, massive nucleus. Electrons, being much lighter, cause negligible deflection. The nucleus's significant mass (R) ensures it remains largely stationary during collision, allowing for large deflections of \(\alpha\)-particles (A).
Assertion (A): A beam of charged particles is employed in the treatment of cancer.
Reason (R): Charged particles on passing through a material medium lose their energy by causing ionization of the atoms along their path.
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; charged particle therapy (e.g., proton therapy) is used for cancer. Reason (R) is true; charged particles lose energy mainly through ionization, creating a Bragg peak that can precisely damage tumor cells. (R) is the correct explanation for (A).
Assertion (A): In sodium nucleus \(_{11}^{23}\text{Na}\), there are no electrons.
Reason (R): Atomic number of sodium is 11.
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
View Answer
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.
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
View Answer
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): 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.
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
View Answer
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.
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 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.
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
View Answer
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.
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
View Answer
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).