Nuclei practice · Medium

Option A (${\mathrm{O}_2}$) is correct because balancing the nuclear reaction requires the product to be an isotope of Oxygen.

Option A (Same number of protons but different number of neutrons) is correct because isotopes have the same atomic number (protons) but different mass numbers (neutrons).

Option C ($10.24 \,\,MeV$) is correct because it is calculated from the mass defect when four Helium nuclei fuse to form one Oxygen nucleus, converted to energy using $E = \Delta m c^2$.

Option B (357 Ci) is correct because the activity is calculated using the half-life, amount, and atomic weight of Au¹⁹⁸.

Option C is correct because in beta decay, the mass number (A) remains the same, while the atomic number (Z) increases by 1.

Option C ($A$) is correct because the volume of a nucleus is directly proportional to its mass number A.

The correct answer is D (Independent of the time of creation) because radioactive decay is a random process and depends only on the decay constant.

Wrong is correct because fission requires a neutron to initiate the reaction, not a proton due to electrostatic repulsion.

Option B is correct because the number of protons is equal to the atomic number (88), and the number of neutrons is the mass number (226) minus the atomic number (88), which equals 138.

Option C (If Assertion is True but the Reason is False) is correct because the assertion about standing waves is correct, but the reason is false as amplitude does depend on position.

Option C ($1:2$) is correct because the ratio of disintegration rates depends on the number of radioactive atoms remaining after two hours, considering their respective half-lives.

Option C ($_{92}{U^{235}}$) is correct because Uranium-235 is the only naturally occurring isotope that is readily fissionable by slow neutrons.

Option C ($8.2 \times 10^{13} J$) is correct because it accurately calculates the energy released from 1 kg of Uranium-235 using the energy per fission and Avogadro's number.

Option B ($M=m_{\text {proton }}+m_{\text {electron }}-\frac{B}{c^2}(B=13.6 {eV})$) is correct because the mass of the hydrogen atom is slightly less than the sum of the masses of its constituents due to binding energy.

Option D (${\mathrm{U}^{238}}$ contains $\mathrm{3}$ more neutrons) is correct because isotopes of an element differ in the number of neutrons.

Option D is correct because radioactive decay is a probabilistic process, and any given nucleus can decay at any time after t=0.

Option B (Both Assertion and Reason are true and Reason is not the correct explanation of Assertion) is correct because both the annihilation process and momentum conservation are true, but the reason doesn't directly explain the annihilation.

Option A (20) is correct because after 2 half-lives, 450 nuclei will have disintegrated from an initial 600.

Option A ($1 . 182 \mathrm{~MeV}$) is correct because it is calculated by finding the mass difference between the parent and daughter nuclei and converting it to energy using $E=mc^2$.

Option B is correct because after each half-life, the amount of substance remaining is halved. After five half-lives, the fraction remaining is (1/2)⁵.

Option C is correct because both the Coulombic (electrostatic) force and the nuclear force act between protons inside the nucleus.