CBSE 2026 · Region 2 · Set 1 · Q22 · 3 marks
(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.
(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
NucleiAtomic Masses and Composition of NucleusUnderstandshort_answermedium
More from Nuclei
- Explain the terms mass defect and binding energy. How are they related?2026 · asked 3×
- (i) Prove that the nuclear density is same for all nuclei. (ii) Draw a plot of potential energy of a pair of…2023 · asked 3×
- Differentiate between nuclear fission and nuclear fusion. Give one example for each with nuclear reaction.2026 · asked 3×
- Assertion: The binding energy per nucleon is practically constant for mass number in the range ( 30<A<170 ).…2025 · asked 3×
- (i) Write any two features of nuclear forces. (ii) If both the number of protons and the neutrons are…2026 · asked 3×
- Assertion: During formation of a nucleus, the mass defect produced is the source of the binding energy of the…2025 · asked 3×
- Which of the following statements is not true for nuclear forces?2023 · asked 3×
- Calculate the energy released in MeV in the following reaction: 1^2 H+ 1^3 H → 2^4 He+n Given: m( 1^2…2022 · asked 3×
CBSE Class 12 Physics past-paper question from the 2026board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.