Nuclei practice · Medium

Option C ($1: 4$) is correct because after 80 minutes, substance A has gone through 4 half-lives and substance B has gone through 2 half-lives, resulting in a ratio of 1/16 to 1/4, which simplifies to 1:4.

Option A (Controlled chain reaction) is correct because atomic reactors are designed to maintain a controlled chain reaction to produce energy safely.

Option A (Nuclei of different elements can have the same number of neutrons) is correct because isotones are defined as having the same number of neutrons but different numbers of protons.

Option B is correct because the size of an atom is on the order of 0.1 to 0.5 nanometers, which is approximately 10^-10 meters.

Option B (The two γ's move in opposite direction) is correct because momentum must be conserved, and since the π⁰ is initially at rest, the two photons must have equal and opposite momenta.

Option C ($1: 1$) is correct because after two hours, the ratio of the activity of X to the activity of Y is 1:1, considering their respective half-lives.

Option C (0.0024) is correct because the mass defect is calculated by dividing the binding energy by 931.5 MeV/amu.

Option C (Tritium) is correct because Tritium is a radioactive isotope of hydrogen.

Option B (7) is correct because it is the binding energy per nucleon calculated from the mass defect using the conversion factor 931 MeV/amu.

Option C (Production of more neutrons in fission) is correct because the release of neutrons during fission sustains the chain reaction.

Option D (Pauli) is correct because Wolfgang Pauli theoretically predicted the existence of the neutrino to explain the missing energy in beta decay.

Option B (78) is correct because the atomic number of the resulting nucleus is calculated by accounting for the changes due to alpha and beta emissions.

Option A ($_1^3H + _1^2H = _2^4He + _0^1n$) is correct because it shows two light nuclei combining to form a heavier nucleus, which is the definition of nuclear fusion.

Option C (1) is correct because after one half-life of A, the rate of disintegration of A is halved, and after two half-lives of B (which is equivalent to one half-life of A), the rate of disintegration of B is also halved, making them equal.

Option C is correct. The density of a nucleus is approximately ${10^{17}} kg/{m^3}$, a remarkably high value.

The correct answer is A (782) because the energy liberated in the beta decay process is calculated using the mass difference between the neutron and its decay products.

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

Option C (Nuclear force is charge dependent) is correct because nuclear force is independent of the charge of the nucleons.

Option A (Nuclear magnetic resonance) is correct because Nuclear Magnetic Resonance (NMR) is the phenomenon where proton flips occur when exposed to a magnetic field and radio frequency radiation.

Option A (Approx $\mathrm{0}\mathrm{.1 }\,\mathrm{\% }$ mass converts into energy) is correct because approximately 0.1% of the mass is converted into energy during nuclear fission.

Option C ($_{26}F{e^{56}}$) is correct because iron-56 has the highest average binding energy per nucleon, making it the most stable nucleus.

Option C ($10^{17} \mathrm{~kg} / \mathrm{m}^3$) is correct because the density of nuclear matter is extremely high, on the order of $10^{17} \mathrm{~kg} / \mathrm{m}^3$.

Option B (Graphite) is correct because graphite is a common moderator used in nuclear reactors to slow down neutrons, increasing the probability of nuclear fission.

Option B (7 s) is correct because the mean life is calculated using the decay constant derived from the given beta particle counts over two consecutive time intervals.

Option A ($510\,\,KeV$) is correct because it is the accepted value for the rest energy of an electron calculated using $E=mc^2$.

Option A ((a) $6.49 \times 10^9 \mathrm{~y};$ (b) $4.5 \times 10^9 \mathrm{~y};$ (c) 4) is correct because it correctly calculates the average life, half-life, and activity decrease factor using the given decay constant.

Option C is correct because the activity of a radioactive sample is directly proportional to the number of radioactive atoms present.

Option A ($2.8 \times 10^9$ disintegrations $\mathrm{s}^{-1}$) is correct because it is calculated by finding the number of Radium atoms and multiplying by the decay constant.

The correct answer is B ($\lambda N$) because the decay rate (R) is directly proportional to the number of radioactive nuclei (N) and the decay constant ($\lambda$).

Option B (20 min) is correct because the time interval between any two percentage decays is equal to the half-life if the percentages are symmetrically placed around 50%.