Nuclear Physics

The multiplication factor in a nuclear reactor refers to the ratio of the number of fissions produced by a given generation of neutrons to the number of fissions in the preceding generation. This factor helps in determining whether the reactor is subcritical, critical, or supercritical. If the multiplication factor is greater than 1, the reactor is supercritical (producing more fissions in each generation), and if it is less than 1, the reactor is subcritical (producing fewer fissions in each generation). When the multiplication factor is equal to 1, the reactor is in a critical state, meaning the number of fissions remains constant from generation to generation.

The correct option is (C) : multiplication factor

The binding energy per nucleon is generally higher for heavier nuclei than for light nuclei. This is because light nuclei like hydrogen or helium have lower binding energies per nucleon compared to heavier nuclei like iron or uranium. As the mass number increases, the binding energy per nucleon also increases, reaching a maximum at iron (Fe). For light nuclei, the average binding energy per nucleon is relatively lower. Thus, the incorrect statement is that the average binding energy per nucleon is very high for light nuclei.

The correct option is (B) : Average binding energy per nucleon is very high for light nuclei.

Step 1: The nuclear radius is given by the empirical formula: where is the mass number and is a proportionality constant.
Step 2: Using the ratio of nuclear radii: Given fermi for and , we compute:
Step 3: Approximating the cube root:
Step 4:
Step 5: Therefore, the correct answer is (A).

Step 1: Isobars are atoms (not necessarily of the same element) that have the same mass number but different atomic numbers.
Step 2: The mass number is defined as the total number of protons and neutrons in an atom's nucleus.
Step 3: Isobars have the same total number of nucleons (protons plus neutrons), which results in the same mass number.
Step 4: Therefore, the defining characteristic of isobars is that they share the same mass number, aligning with option (B).

In nuclear fusion, the mass of the product nucleus is always less than the sum of the masses of the fusing nuclei and . This is due to the fact that some of the mass is converted into energy, as per the mass-energy equivalence principle .
Thus, the correct answer is (A).

In intrinsic semiconductors, the product of the electron concentration and hole concentration is equal to the square of the intrinsic carrier concentration : This relation holds because in an intrinsic semiconductor, the number of electrons is equal to the number of holes.
Thus, the correct answer is (A).

At absolute zero temperature , all the electrons in an intrinsic semiconductor are in the valence band and there are no free electrons in the conduction band.
Hence, it behaves like an insulator because no charge carriers are available for conduction.
Thus, the correct answer is (A).