An alpha particle is launched at a stationary nickel nucleus. An alpha particle

Question

An alpha particle is launched at a stationary nickel nucleus. An alpha particle is a doubly ionized helium nucleus, so it has the charge of two protons and the mass of 4 amu. The nickel nucleus has the charge of 28 protons and the mass of 56.69 amu. 1 amu (atomic mass unit) has a mass of 1.66•10-27 kg. Assume the collision to be perfectly elastic and occurring along a line passing through the center of mass of both particles such that there is no rotational motion.

a) If the alpha particle has an initial kinetic energy of 5.68 MeV, find the minimum distance that separates the alpha particle and the nickel nucleus. You may not ignore the recoil of the nucleus in your calculation.

Explanation / Answer

ECM = [(E*mNi)/(m*mNi)] = [(5.68*10^6*1.6*10^-19*56.69*1.66*10^-27)/(4*1.66*10^-27*56.69*1.66*10^-27)] = 8.5*10^-13 J

rc = [(kZNiZqe2)/(ECM)] = [(9*10^9*28*2*(1.6*10^-19)2)/( 8.5*10^-13)] = 1.5*10^-14 m = 15fm

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