7.9 MeV α -particle scatters from a target material of atomic number… | JEE Main 2026 (22 Jan, Shift 1)

Q3JEE Main 2026 · 22 JAN · SHIFT 1Medium

Atomic Models & Alpha-Particle Scattering

$7.9\text{ MeV }\alpha$ -particle scatters from a target material of atomic number 79. From the given data the estimated diameter of nuclei of the target material is (approximately) ______ m.

$\Bigg[\frac{1}{4\pi\epsilon_0} = 9 \times 10^{9}\text{ Nm}^2/\text{C}^2$ and electron charge $= 1.6 \times 10^{-19}\text{ C}\Bigg]$

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Answer: (b)

Closest approach: $r_0 = \dfrac{k(2e)(Ze)}{K}$ with $K = 7.9\text{ MeV} = 7.9\times10^6 e$ J.
$r_0 = \dfrac{9\times10^9 \times 2 \times 79 \times 1.6\times10^{-19}}{7.9\times10^6} = 2.88\times10^{-14}$ m.
This estimates the nuclear radius, so diameter $= 2r_0 = 5.76\times10^{-14}$ m.
So the answer is (b).

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