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.
Assertion (A): Energy is released when heavy nuclei undergo fission or light nuclei undergo fusion.
Reason (R): For heavy nuclei, binding energy per nucleon increases with increasing (Z) while for light nuclei, it decreases with increasing (Z).
Assertion (A) is true as both fission and fusion release energy. Reason (R) is false because binding energy per nucleon for heavy nuclei decreases with increasing (Z) (after Fe) and increases for light nuclei (up to Fe). Thus, (A) is true, (R) is false.
Assertion (A): Size of nucleus determined electron scattering and (alpha)-scattering are same.
Reason (R): Electron scattering or by (alpha)-scattering is controlled by distribution of charge in nucleus.
Assertion (A) is true; both methods estimate nuclear size based on charge distribution. Reason (R) is true; both electron and alpha scattering probe nuclear charge distribution. (R) correctly explains (A) as the interaction with charge distribution determines the 'size' measured.
Assertion (A): It is very easy to detect neutrino in nature.
Reason (R): It has high affinity to interact with matter.
Assertion (A) is false; neutrinos are extremely difficult to detect due to very weak interactions. Reason (R) is also false; neutrinos have very low affinity to interact with matter. Therefore, both (A) and (R) are false.
Assertion (A): More energy is released in fusion than fission per nucleon.
Reason (R): More number of nucleons takes part in fusion.
Assertion (A) is true; fusion releases significantly more energy per nucleon than fission. Reason (R) is false; fusion involves lighter nuclei (fewer nucleons) compared to fission.
The higher energy release per nucleon is due to the greater increase in binding energy per nucleon.
Assertion (A): Deuterium is a good moderator of fast neutrons.
Reason (R): Fast neutrons transfer 90% of their kinetic energy to the nuclei of the moderator in an elastic collision.
Assertion (A) is true. Deuterium's mass is close to a neutron's, making it efficient for moderation. Reason (R) is true; in elastic collision with deuterium, neutrons lose about 89% of their kinetic energy. (R) is the correct explanation for (A).
Assertion (A): Beryllium can be used as a moderator in nuclear fission reactor.
Reason (R): A fast moving electron on collision with a light stationary particle loses most of its energy in nuclear reactor.
Assertion (A) is true; Beryllium is a suitable moderator due to low mass and absorption.
Reason (R) is false; moderation involves neutrons, not electrons. Electrons are not used for moderating neutrons in nuclear reactors. Thus, (A) is true, but (R) is false.