7.9 MeV -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. [2026]

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Solution

Q.
7.9 MeV $α$ -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.

$[\frac{1}{4 π ε_{0}} = 9 \times 10^{9} {Nm}^{2} / C^{2} and electron charge = 1.6 \times 10^{- 19} C]$ [2026]

1 $1.44 \times 10^{- 13}$

2 $2.88 \times 10^{- 14}$

3 $1.69 \times 10^{- 12}$

4 $5.76 \times 10^{- 14}$

Ans.
(4)

$By mechanical energy conservation$

${(ME)}_{i} = {(ME)}_{f}$

$P E_{i} + K E_{i} = P E_{f} + K E_{f}$

$0 + 7.9 \times 10^{6} \times 1.6 \times 10^{- 19} = \frac{k (2 e) (Z e)}{r} + 0$

$r = \frac{9 \times 10^{9} \times 2 \times {(1.6 \times 10^{- 19})}^{2} \times 79}{7.9 \times 10^{6} \times 1.6 \times 10^{- 19}} = 2.88 \times 10^{- 14} m$

$For diameter \Rightarrow D = 2 r = 5.76 \times 10^{- 14} m$

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