Consider a Rutherford scattering experiment in which an alph

Consider a Rutherford scattering experiment in which an alpha particle is fired at a sheet of atoms only one atomic layer thick (see the figure below). The radius of an alpha particle is about 1 fm (1 ? 10?15 m) and assume the radius of the nuclei in the figure has the same value. Also assume the spacing between atoms in the sheet is 0.2 nm.

(a) If alpha particles are fired at random at the sheet, what is the probability that one will strike a nucleus? (Assume that the center of an alpha particle must overlap with a carbon nucleus for a collision to occur.)

(b) If one trillion (1012) alpha particles are fired, about how many will hit a nucleus? (State your answer to at least the nearest integer.)

Alpha particles 0 o--> o Nucleus Nucleus 0-

Solution

Here,

radius of alpha particle, r = 1 *10^-15 m

distance between the atoms , R = 0.2 nm

R = 2 *10^-10 m

a) as the area in which fired aplha particle will strike the nuclues is 2r

probability that one will strike a nucleus = pi * (2r)^2/( pi * R^2)

probability that one will strike a nucleus = (2 * 10^-15)^2/(2 *10^-10)^2

probability that one will strike a nucleus = 1 *10^-10

the probability that one will strike a nucleus is 1 *10^-10

b)

number of alpha particle , N = 10^12

number of alpha particles striking the nucleus = probability * number of alpha particles

number of alpha particles striking the nucleus = 10^12 * 1 *10^-12

number of alpha particles striking the nucleus = 100

the number of alpha particles striking the nucleus is 100