Nuclei practice · Mixed difficulty

Option D (Statement-I is false and Statement-II is true) is correct because a positive packing fraction implies a smaller binding energy, and the packing fraction is related to the mass defect, not the mass number.

Option A (1.23) is correct because it is the approximate ratio calculated using the formula relating nuclear radius and mass number.

Option D (The nuclear force becomes very strong if the nucleus contains a large number of nucleons) is the WRONG statement because while nuclear force is strong, adding too many nucleons can lead to instability.

Option A is correct because the mass of the nucleons (protons and neutrons) when separate is greater than the mass of the nucleus they form due to the binding energy.

Option B is correct because nuclear density is independent of mass number.

Option B (possible only inside the nucleus) is correct because the neutron is more massive than the proton, and this mass difference can be compensated by the binding energy inside the nucleus.

Option D (First increases and then decreases with increases of mass number) is correct because the binding energy per nucleon initially increases, reaches a peak, and then gradually decreases as the mass number increases.

Option C is correct because nuclear density is independent of the mass number.

Option C (10) is correct because the half-life is calculated by finding the number of half-lives in the given time and dividing the total time by that number.

Option C ($\frac{\left(t_2-t_1\right)}{2 \ln (R)}$) is correct because it correctly relates the average life to the given activities at times $t_1$ and $t_2$.

Option C ($6.03\,g$) is correct because after 20 years, approximately 6.03g of the radioactive material will have disintegrated.

Option B ($\mathrm{16}\mathrm{.5 }\,\mathrm{days}$) is correct because it is calculated using the half-life formula and the given logarithmic value.

Option A (Protons) is correct because protons are not typically emitted during radioactive decay processes such as alpha, beta, or gamma decay.

Option C (1:1) is correct because nuclear density is approximately constant for all nuclei, independent of mass number.

Option B ($20\,\,\min$) is correct because it is the approximate difference in time between 33% and 67% disintegration, calculated using the half-life formula.

Option B (Liquid drop model) is correct because the liquid drop model of the nucleus explains nuclear fission by treating the nucleus as a liquid drop.

Option C (larger for fission fragments than for parent nucleus) is correct because nuclear energy is released in fission due to the higher binding energy per nucleon in the fragments.

Option C (The biological effect of radiation) is correct because the rad is a unit used to measure the absorbed dose of radiation, which is related to its biological effect.

Option D (Equal to sum of masses of two protons and two neutrons) is incorrect because the mass of an alpha particle is less than the sum of the masses of its constituent protons and neutrons due to the binding energy.

Option A ($28.4 M e V$) is correct because it is the binding energy calculated using the mass defect and the energy equivalent.

Option D (17.3 MeV) is correct because it is the energy released in the nuclear reaction, calculated from the difference in binding energies.

Option C is correct because in nuclear fusion, some mass is converted into energy, resulting in the mass of the resultant nucleus being less than the sum of the masses of the fusing nuclei.

The correct answer is 32 min. The half-life is calculated by finding the time it takes for the decay rate to halve.

Option A (Neutron into a proton) is correct because a $\beta^{-}$ particle emission occurs when a neutron in the nucleus transforms into a proton, releasing an electron ($\beta^{-}$ particle) and an antineutrino.

Option A (iron) is correct because iron (Fe) has the highest binding energy per nucleon among common elements, making it the most stable nucleus.

Option B is correct. Both the assertion and the reason are true, but the reason is not the correct explanation of the assertion. The constant nuclear density arises from the short-range nature of the strong nuclear force, not directly from the radius formula.

A current will flow from A to B because alpha particles are positively charged and beta particles are negatively charged, creating a potential difference.

Option D is incorrect. Most suitable element for nuclear fission is the element with atomic number near 92.

Option C is correct because radioactive decay is a random process, so the number of atoms remaining in each container will vary, but the average will be close to 5000.

Option B is correct because the half-life is given by $\frac{{\log_e 2}}{\lambda}$ and the mean life is given by $\frac{1}{\lambda}$.