trying to look for a derivation of the Rutherford scattering formula from Hyperphysics, but cannot find one. It doesn't show up in the original paper How is this equation derived?

Dillan Valenzuela

Dillan Valenzuela

Answered question

2022-08-14

Trying to look for a derivation of the Rutherford scattering formula from Hyperphysics, but cannot find one. How is this equation derived?
N ( θ ) = N i n L Z 2 k 2 e 4 4 r 2 K E 2 sin 4 ( θ / 2 )
where
N i is the number of incident alpha particles
n is the number of atoms per unit volume in the target
L is the thickness of the target
Z is the atomic number of the target
e is the electron charge
k is Coulomb's constant
r is the target-to-detector distance
K E is the kinetic energy of the alpha particle
θ is the scattering angle

Answer & Explanation

Siena Bennett

Siena Bennett

Beginner2022-08-15Added 17 answers

Rutherford scattering the derivation of the scattering cross section
d σ d Ω = ( Z 1 Z 2 e 2 8 π ϵ 0 m v 0 2 ) 2 csc 4 ( Θ 2 )
is given. Let's rewrite that in your notation: Z 1 = Z, Z 2 = 4, k = 1 4 π ε 0 and K E = 1 2 m v 2 :
d σ d Ω = ( Z e 2 k K E ) 2 csc 4 ( Θ 2 ) = Z 2 k 2 e 4 K E 2 sin 4 ( θ / 2 )
The relation between the cross section and the number of detected particles is
N ( θ ) N i = n L 4 r 2 d σ d Ω
n L gives the number of targets to scatter from and 1 / ( 4 r 2 ) is because at a bigger distance the intensity goes down by this factor.

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Nuclear physics

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?