Rajasthan Board Class 12 (RBSE) Nuclei — practice questions

1. syllabus defines the unified atomic mass unit by international convention. 2. The reference standard is the neutral atom of carbon-12, $\,^{12}_{6}\mathrm{C}$, in its electronic ground state. 3. One unified atomic mass unit: $1\,u = \dfrac{1}{12}\,m(\,^{12}_{6}\mathrm{C}) = 1.66054\times 10^{-27}\,\text{kg}$. 4. Carbon-12 was chosen in 1961 because it gives integer-friendly mass values for most elements. 5. Options A, C, D were never the standard — though older systems (pre-1961) used $\,^{16}\mathrm{O}$ for chemistry (option C), this gave a slightly different unit than physics's $\,^{16}\mathrm{O}$ isotope-only definition. _Source: syllabus Physics Part 2, Ch 13 "Nuclei", §13.2 (Atomic Masses), p. 1._

1. The mass defect captures the fact that an assembled nucleus weighs LESS than the sum of its free constituents — the "missing" mass shows up as the nuclear binding energy. 2. syllabus defines: $\Delta m = (\text{sum of nucleon masses}) - M_{\text{nucleus}}$. 3. Sum of free nucleon masses: $Z$ protons of mass $m_p$ plus $(A-Z)$ neutrons of mass $m_n$, giving $Z m_p + (A-Z) m_n$. 4. Subtract the actual nucleus mass $M$: $\Delta m = Z m_p + (A-Z) m_n - M$. 5. By construction, $\Delta m > 0$ for any stable nucleus. Option A has the sign reversed. Options C, D don't represent the right combination of free constituents. _Source: syllabus Physics Part 2, Ch 13, §13.4 (Mass-Energy and Nuclear Binding Energy, definition of mass defect), p. 5._

1. Use Einstein's mass-energy relation $E = mc^2$. 2. syllabus computes: $1\,u = 1.66054\times 10^{-27}\,\text{kg}$, $c = 2.998\times 10^{8}\,\text{m/s}$. 3. $E = (1.66054\times 10^{-27})(2.998\times 10^{8})^2 = 1.4924\times 10^{-10}\,\text{J}$. 4. Convert to MeV: $1\,\text{MeV} = 1.602\times 10^{-13}\,\text{J}$, so $E = \dfrac{1.4924\times 10^{-10}}{1.602\times 10^{-13}} = 931.5\,\text{MeV}$. 5. This number is THE standard conversion used in nuclear physics: $1\,u \leftrightarrow 931.5\,\text{MeV}/c^2$. It appears in every nuclear binding-energy calculation. 6. Option A is just $1\,\text{eV}$ in joules (confusing constants). Option C is the numerical value of $u$ itself (in kg) misread as eV. Option D is the typical BE/nucleon value, not the u-equivalent. _Source: syllabus Physics Part 2, Ch 13, Example 13.3, p. 6._