Nuclei practice · Medium

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 $\frac{1}{\lambda}$.

Option A (Statement-I and Statement-II are true) is correct because nuclei around mass number 60 are indeed the most stable, and fusion of lighter nuclei increases the binding energy per nucleon.

Option A ($3: 16$) is correct because it correctly calculates the ratio of disintegration rates after 18 hours using the given half-lives.

Option B (20 minutes) is correct because the time between 33% decay and 67% decay is equal to one half-life, as it represents the time it takes for the remaining amount to halve from 67% to 33.5% (approximately 33%).

Option C (Neutrons) is correct because free neutrons are unstable and decay with a relatively short mean lifetime.

Option D (1) is correct because after accounting for alpha decay, one beta particle emission is needed to match the final atomic number.

Option A (${T_B} < {T_A}$) is correct because of time dilation in special relativity. The observer moving with the asteroid measures the proper time, which is shorter than the time measured by a stationary observer.

Option A is correct because the mass of a nucleus is always less than the sum of the masses of its constituent nucleons due to the binding energy.

Option C (15 days) is correct because after 15 days, 7/8th of the sample decays, leaving 1/8th, which is three half-lives.

Option D ($\mathrm{1:1}$) is correct because the nuclear density is independent of the mass number.

Option C (₈₃X²¹⁶) is correct because it correctly accounts for the decrease in mass number and atomic number due to the emission of 3 alpha particles and 1 beta particle.

Option B is correct because the fusion of Helium-3 nuclei is a primary energy source in the sun.

Option D (0.125) is correct because the recoil energy of the daughter nucleus is calculated using the conservation of momentum.

Option D is correct because when a neutron decays into a beta particle (electron), it also produces a proton and an antineutrino to conserve charge and lepton number.

Option C (III only) is correct because the photoelectric theory states that the number of photoelectrons emitted depends on the frequency, not the intensity, of the light.

Option B is correct because energy released in a chemical reaction comes from changes in the binding energy of the electrons in the atoms and molecules involved.

Option A (Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A)) is correct because fission releases energy due to higher binding energy of fragments.

Option A ($\alpha$ and $\beta^{-}$) is correct because both alpha and beta-minus decay change the number of protons in the nucleus, thus creating a new element.

Option A (0.707) is correct because after half of a half-life, the remaining fraction is $1/\sqrt{2}$ which is approximately 0.707.

Option C (Absorb some neutrons) is correct because cadmium rods are used to control the chain reaction by absorbing neutrons.

Option A ($\frac{{{T_B}}}{{{T_A}}}$) is correct because the half-life of a radioactive element is inversely proportional to its decay constant, so the ratio of decay constants is the inverse of the ratio of half-lives.