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Nuclei

Question
CBSEENPH12039739

An α-particle of energy 5 MeV is scattered through 180° by a fixed uranium nucleus. The distance of the closest approach is of the order of

  • 1 Å

  • 10−10 cm

  • 10−12 cm

  • 10−15 cm

Solution

C.

10−12 cm

At closest approach, all the kinetic energy of the α-particle will converted into the potential energy of the system, K.E. = P.E.
straight i. straight e. space 1 half space mv squared space equals space fraction numerator 1 over denominator 4 πε subscript 0 end fraction fraction numerator straight q subscript 1 straight q subscript 2 over denominator straight r end fraction
5 space MeV space equals space fraction numerator 9 space straight x space 10 to the power of 9 space straight x space left parenthesis 2 straight e right parenthesis space straight x space 92 straight e over denominator straight r end fraction space open parentheses therefore space 1 half space mv squared space equals space 5 space MeV close parentheses

rightwards double arrow space straight r space equals space fraction numerator 9 space straight x space 10 to the power of 9 space straight x space 2 space straight x 92 space straight x space left parenthesis 1.6 space straight x space 10 to the power of negative 19 end exponent right parenthesis squared over denominator 5 space straight x space 10 to the power of 6 space straight x space 1.6 space straight x space 10 to the power of negative 19 end exponent end fraction
straight r space equals space 5.3 space straight x space 10 to the power of negative 14 end exponent space straight m space equals space 10 to the power of negative 12 space cm end exponent