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For scattering by an inverse-square fiel...

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, the scattering angle for `b=0` is

A

`180^(@)`

B

`90^(@)`

C

`45^(@)`

D

`120^(@)`

Text Solution

Verified by Experts

The correct Answer is:
A
given `b=0`
`therefore =(Ze^2co t(theta)/2)/(4piepsilon_0(1/2mv^2))=0` or `co t(theta)/(2)=0`
`[because "All other quantities are finite"]`
`therefore(theta)/(2)=90^@` or `theta=180^@`
Which is the value expected physically for a head- on collision.
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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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In Rutherford scattering experiment, wha will be the ratio of impact parameter for scattering angles theta_(1)=90^(@) and theta_(2)=120^(@)