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Physics · 2023 · 3 marks
CBSE 2023 · Region 3 · Set 1 · Q30
(a) (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…
(a)(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.
OR
(b)(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
(a)(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.
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CBSE Class 12 Physics past-paper question from the 2023 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.