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Physics · 2026 · 3 marks
CBSE 2026 · Region 2 · Set 1 · Q22
(a) Consider the following nuclides: _6^12 C,_80^198 Hg,_6^14 C,_79^197 Au Group them into isotopes and isotones. (b) How does the size of a nucleus…
(a)
Consider the following nuclides : \[{ }_{6}^{12} \mathrm{C},{ }_{80}^{198} \mathrm{Hg},{ }_{6}^{14} \mathrm{C},{ }_{79}^{197} \mathrm{Au} \] Group them into isotopes and isotones.
(b)
How does the size of a nucleus depend on its mass number A ? Hence prove that the density of nucleus is a constant, independent of A, for all nuclei.
Marking-scheme solution
(a)
Isotopes: $\displaystyle { }_{6}^{12} \mathrm{C},{ }_{6}^{14} \mathrm{C}$
Isotones: $\displaystyle { }_{80}^{198} \mathrm{Hg},{ }_{79}^{197} \mathrm{Au}$
(b)
Size of nucleus $\displaystyle \propto \mathrm{A}^{1 / 3}$ (Alternatively: $\displaystyle \mathrm{R}=\mathrm{R}_{0} \mathrm{~A}^{1 / 3}$)
Suppose $\displaystyle m$ is the average mass of a nucleon, density of nucleus $\displaystyle \rho=\dfrac{\text{Mass}}{\text{Volume}}$
$\displaystyle \rho=\dfrac{m \mathrm{A}}{\frac{4}{3} \pi\left(\mathrm{R}_{0} \mathrm{~A}^{1 / 3}\right)^{3}}$
$\displaystyle \rho=\dfrac{3 m}{4 \pi \mathrm{R}_{0}^{3}}=$ constant
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CBSE Class 12 Physics past-paper question from the 2026 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.