Consider the scattering of an alpha particle from the positively charged part of
ID: 1879914 • Letter: C
Question
Consider the scattering of an alpha particle from the positively charged part of the Thomson plum pudding model. Let the kinetic energy of the particle be K (nonrelativistic) and let the atomic radius be R. (a) Assuming that the maximum transverse Coulomb force acts on the a particle for a time 1 2R/v (where v is the initial speed of the particle), show that the largest scattering angle we can expect from a single atom is (b) Evaluate 0 for an 8.0-MeV a particle scattering from a gold atom of radius 0.135 nm.Explanation / Answer
a) For a
The maximum Coulomb force is at the surface can be calculated by putting all the charge at the centre of the sphere and is therefore equal to Z1Z2 e2/40R2, with Z1 = 2 .
Then
p = Ft
= Z1Z2 e2 /40R2 *2R/ v
=e2/40 *2Z1Z2/Rv
Using the same argument as that leading to above equation we find the maximum angular deflection, for small angles, with
=tan = p/p
= 2Z2e2/40KR
b) For an 8.0-MeV particle scattering from a gold atom ( Z2 = 79 ) of radius 0.135 nm we find that
= 2Z2e2/40KR
= (2) (79) (1.44 eVnm) / (8 MeV) (0.135 nm) = 2.11×104 rad = 0.012 degree