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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 anglethetais given byb (Ze^2 cot (theta/2))/(4 pi epsi_0 ((mv^2)/(2))) a. What is the scattering angle for b =0? b. For a given impact parameter h, does the angle of deflection increase or decrease with increasing energy? c .What is the impact parameter at which the scattering angle is 90^@ for Z = 79 and initial energy of 10 MeV? d. Why is it that the mass of the nucleus does not enter the formula above but the 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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Answer» Solution :a.For b = 0, we get cot ` theta /2` = 0. It means` theta /2 = 90^@ `or 0= `180^@ ` b. Increase in b means increase in cot.`theta /2` i.E., decrease in `theta `. c. USING `b =(Ze^2 cot "" theta /2)/( 4pi epsi_0E )`, we get b= `1.1 xx 10^(-14)` m d. Scattering occurs because of field due to the CHARGE on nucleus. If Z=0, then `theta `=0. As recoilof nucleousis notconsider, domassofnueleousunimportant butin case RECOIL is not ignored, then small change in the relation is required. e. Decrease in b means decrease in cot `theta /2`i.e., increase in scattering angle `theta`. |
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