Assertion (A): The value of Rydberg constant is independent of mass of nucleus.
Reason (R): Electrons revolve around stationary nucleus of atom.
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.
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.
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.
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.
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 \( \text{U}^{235} \).
\( \text{Fe}^{56} \) 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.
Assertion (A): Electron capture occurs more often than positron emission in heavy elements.
Reason (R): Heavy elements exhibit radioactivity.
In heavy nuclei, electron capture is favored over positron emission. So (A) is true. Heavy elements are generally unstable and radioactive. So (R) is true. However, (R) does not explain the preference for electron capture.
Assertion (A): A nuclei has mass more than the sum of the masses of the individual nucleons in them.
Reason (R): In nuclei, number of neutrons is less than the number of electrons.
Assertion (A) is false because of mass defect; the nucleus mass is less than the sum of constituent nucleons. Reason (R) is false as neutrons are in the nucleus and electrons orbit outside. Thus, both (A) and (R) are false.
Assertion (A): Isotopes of an element can be separated by using a mass spectrometer.
Reason (R): Separation of isotopes is possible because of the difference in electron numbers of isotopes.
Assertion (A) is true; mass spectrometers separate particles based on mass-to-charge ratio, and isotopes have different masses. Reason (R) is false; isotopes of an element have the same number of electrons (in a neutral atom) and differ in neutron numbers, not electron numbers.
Assertion (A): Nuclear binding energy per nucleon is in the \( {}^{8}_{4}\text{Be} > {}^{7}_{3}\text{Li} > {}^{4}_{2}\text{He} \).
Reason (R): Binding energy per nucleon increases linearly with difference in number of neutrons and protons.
Assertion (A) is false; \( {}^{4}_{2}\text{He} \) has a significantly higher binding energy per nucleon than \( {}^{7}_{3}\text{Li} \) and particularly unstable \( {}^{8}_{4}\text{Be} \). Reason (R) is false; binding energy per nucleon does not increase linearly with the N-P difference. Both (A) and (R) are false.