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For scattering by an .inverse square. field (such as that produced by a charged nucleus in Rutherford.s model), the relation between impact parameter b and the scattering angle theta is given by, b=(Ze^(2)cot theta//2)/(4pi epsilon_(0)((1)/(2)mv^(2))) What is the impact parameter at which the scattering angle is 90^(@) for Z = 79 and initial energy equal to 10MeV ? |
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Answer» Solution :Given relation: `b=(ZE^(2)cot theta//2)/(4pi epsilon_(0)((1)/(2)mv^(2)))` `theta=90^(@),Z=79,e=1.6xx10^(-19)C` Now `E=(1)/(2)mv^(2)=10MeV` `=10xx10^(6)xx1.6xx10^(-19)J=1.6xx10^(-12)J` `:.b=(9xx10^(9)xx79xx(1.6xx10^(-19))^(2)cot 45^(@))/(1.6xx10^(-12))` `=1.1xx10^(-14)m` |
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