CBSE 2023 · Region 3 · Set 1 · Q30 · 3 marks
(i)Prove that the nuclear density is same for all nuclei.(ii)Draw a plot of potential energy of a pair of nucleons as a function of their separation. Draw two inferences from this plot.(i)Draw a graph to show the variation of the number of scattered particles detected ( N ) in Geiger-Marsden experiment as a function of scattering angle ( $\displaystyle \theta$ ).(ii)Discuss briefly two conclusions that can be drawn from this graph and how they lead to the discovery of nucleus in an atom.
(i)
Prove that the nuclear density is same for all nuclei.
(ii)
Draw a plot of potential energy of a pair of nucleons as a function of their separation. Draw two inferences from this plot.
(i)
Draw a graph to show the variation of the number of scattered particles detected ( N ) in Geiger-Marsden experiment as a function of scattering angle ( $\displaystyle \theta$ ).
(ii)
Discuss briefly two conclusions that can be drawn from this graph and how they lead to the discovery of nucleus in an atom.
Marking-scheme solution
(i)
\(\displaystyle \rho=\frac{\text { mass }}{\text { volume }}\)
\[=\frac{\text { mass number } \text { × } \text { mass of nucleon }}{\text { volume of nucleus }}
\]
\[\rho=\frac{A \times \mathrm{m}}{\dfrac{4}{3} \pi\left(R_{0} A^{1 / 3}\right)^{3}}=\frac{3 \mathrm{m}}{4 \pi R_{\mathrm{o}}^{3}}
\]
Hence, density is independent of mass number.
(ii)
Inferences
-The force is attractive for distances larger than \(\displaystyle \mathrm{r}_{\mathrm{o}}\).
The force is repulsive for distance less than \(\displaystyle \mathrm{r}_{\mathrm{o}}\).
Alternatively:-
Any other relevant inference drawn from the graph should be given full credit.
NucleiSize of the NucleusUnderstandshort_answerhard
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CBSE Class 12 Physics past-paper question from the 2023board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.