CBSE 2026 · Region 3 · Set 3 · Q28 · 3 marks
A deuterium nucleus and an alpha particle approach a target nucleus separately in head-on position. Find the ratio of their distance of closest approach to the nucleus, when both have :(a)the same velocity, and(b)the same momentum.
A deuterium nucleus and an alpha particle approach a target nucleus separately in head-on position. Find the ratio of their distance of closest approach to the nucleus, when both have :
(a)
the same velocity, and
(b)
the same momentum.
Marking-scheme solution
$\displaystyle \dfrac{1}{2} \mathrm{mv}^{2}=\dfrac{k \mathrm{q}_{1} \mathrm{q}_{2}}{\mathrm{d}}$
(a)
$\displaystyle \mathrm{d} \propto \dfrac{\mathrm{q}}{\mathrm{m}}$ (for the same velocity)
$\displaystyle \dfrac{\mathrm{d}_{\text{deuteron}}}{\mathrm{d}_{\alpha}}=\dfrac{\mathrm{q}_{\text{deuteron}}}{\mathrm{q}_{\alpha}} \times \dfrac{\mathrm{m}_{\alpha}}{\mathrm{m}_{\text{deuteron}}}=\dfrac{e}{2 e} \times \dfrac{4 m}{2 m}=1$
$\displaystyle \mathrm{d}_{\text{deuteron}}: \mathrm{d}_{\alpha}=1: 1$
(b)
$\displaystyle \dfrac{p^{2}}{2 m}=\dfrac{k \mathrm{q}_{1} \mathrm{q}_{2}}{\mathrm{~d}}$, so $\displaystyle d \propto q m$ (for the same momentum)
$\displaystyle \dfrac{\mathrm{d}_{\text{deuteron}}}{\mathrm{d}_{\alpha}}=\dfrac{\mathrm{q}_{\text{deuteron}} \times \mathrm{m}_{\text{deuteron}}}{\mathrm{q}_{\alpha} \times \mathrm{m}_{\alpha}}=\dfrac{e \times 2 m}{2 e \times 4 m}=\dfrac{1}{4}$
$\displaystyle \mathrm{d}_{\text{deuteron}}: d_{\alpha}=1: 4$
NucleiSize of the NucleusApplyshort_answerhard
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.