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Impact Parameter

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A dparticle of mas m moving with speed u collides elastically with a sphere of radius R and same mass at rest, at an impact parameter d. Find (a) Angle between their final velocities and (b) Magpitude of their final velocities.

A proton of mass m moving with a speed v_(0) apporoches a stationary proton that is free to move. Assuming impact parameter to be zero., i.e., head-on collision. How close will be incident proton go to other proton ?

A disk A of radious r moving on perfectly smooth surface at a speed v undergoes an elastic collision with an identical stationary disk B. Find the velocity of the disk B after collision if the impact parameter is r//2 as shown in the figure :-

Figure shows a charge +Q clamped at a point in free space. From a large distance another charge particle of charge -q an.d mass m is thrown toward +Q with an impact parameter d as shown with speed v. Find the distance of closest approach of the two particles.

A projectile of mass m, charge Z', initial speed v and impact parameter b is scattered by a heavy nucleus of charge Z. Use angular momentum and energy conservation to obtain a formula connecting the minimum distance (s) of the projectile form the nucleus to these parameters .show that for b=0, s reduces to the closest distance of approach r_0 .

There is a fixed sphere of radius R having positive charge Q uniformly spread in its volume. A small particle having mass m and negative charge (– q) moves with speed V when it is far away from the sphere. The impact parameter (i.e., distance between the centre of the sphere and line of initial velocity of the particle) is b. As the particle passes by the sphere, its path gets deflected due to electrostatics interaction with the sphere. (a) Assuming that the charge on the particle does not cause any effect on distribution of charge on the sphere, calculate the minimum impact parameter b0 that allows the particle to miss the sphere. Write the value of b_(0) in term of R for the case 1/2mV^(2)=100.((kQq)/(R)) (b) Now assume that the positively charged sphere moves with speed V through a space which is filled with small particles of mass m and charge – q. The small particles are at rest and their number density is n [i.e., number of particles per unit volume of space is n]. The particles hit the sphere and stick to it. Calculate the rate at which the sphere starts losing its positive charge (dQ)/(dt). Express your answer in terms of b_(0)

The following text gives a qualitative idea about Rutherford's alpha- particle scattering experiment. Applying some trigonometry and calculus, Rutherford got the following equation: cot ((0)/(2)) = (Kxx(KE))/(Ze^(2))xxb "where", K= "constant" =((1)/(9xx10))(c^(2))/(N-m^(2)) KE = initial kinetic energy of alpha- particle, e=1.6xx10^(-19)C In an experment with gold nucleus (assume Z=80) with impact parameter equal to 10^(-4)m the scattering angle was found to be 90^(@), What should be the initial KE of alpha- particle?