41.
Alpha particles having kinetic energy of 1.8 MeV each are incident on a thin gold foil, form a large distance. Applying the principle of conservation of energy, find the closest distance of approach of the alpha particle from the gold nucleus.
Kinetic energy of α-particle = Potential energy of repulsion between α-particle and nucleus.
![straight K. straight E. space equals space fraction numerator 9 space straight x space 10 to the power of 9 space left parenthesis straight Z subscript straight e right parenthesis space 2 straight e over denominator straight r subscript straight e end fraction
1.8 space MeV equals space fraction numerator 9 space straight x space 10 to the power of 9 space left parenthesis Ze right parenthesis thin space 2 straight e over denominator straight r subscript straight o end fraction
straight r subscript straight o space equals space fraction numerator 9 space straight x space 10 to the power of 9 space straight x space 2 space straight x space Ze squared over denominator 1.8 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
space space space equals space fraction numerator 9 space straight x space 10 to the power of 9 space straight x space 2 space straight x space 79 space straight x space left parenthesis space 1.6 space straight x space 10 to the power of negative 19 end exponent right parenthesis space squared over denominator 1.8 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
space space space equals space fraction numerator 3640 space. space 32 space straight x space 10 to the power of 9 space straight x space 10 to the power of negative 36 end exponent over denominator 2.88 space straight x space 10 to the power of 6 space straight x space 10 to the power of negative 19 end exponent end fraction](/application/zrc/images/qvar/IPHEN12114114.png)
= 1264 x 10 -16
r0 = 1.264 x 10-13m
The distance of closest approach is 1.264 x 10-13 m.
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