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The impact parameter at which the scatte...

The impact parameter at which the scattering angle is `90^(0) , z=79` and initial energy `10MeV` is

A

`1.137xx10^(-14)`m

B

`1.137xx10^(-16)m`

C

`2.24xx10^(-17)`m

D

`2.24xx10^(18)`m

Text Solution

Verified by Experts

The correct Answer is:
A
`b=(ze^(2)cot(theta//2))/(4piepsilon_(0)xxE)`
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for scattering by an inverse square law 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 in_0(1/2mv^2)) (a) What is the scattering angle for b=0? (b) for given impact parameter, b, does the angle of deflection increase or decrease with increase in energy? (c) What is the impact parameter at which the scattering angle is 90^@ for Z=79 and initial energy=10MeV? (d) Why is it that the mass of the nucleus does not enter the formula above, but its charge does? (e) for a given energy of the projectile, does the scattering angle increase or decrease with decrease in impact parameter?

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