Rutherford Scattering -scattering angle and formula

[prehisto]

Homework Statement

Given variables and data: flux of alpha particles;Z; T-kinetic energy of the flux;
t-thickness of the target.I have to calculate the number of alpha particles which are
scattered in angle θ>60 degrees.

Homework Equations

1) Is my formula correct ( see below) if I am including the T-kinetic energy ?
2) Do i have to integrate the solid angle element dΩ from 60 to 360 degrees?
3) What kind of value should I put in the sin^4(θ/2)- do I have to integrate this part as well ?

The Attempt at a Solution

dN/N=n ((Ze^2)/(8 Pi ε T))^2 dΩ/(sin^4(θ/2))
Where θ-scattering angle
ε-electric constant
n-atoms per unit volume in target
e-electron charge

 

[anathema]

First of all, it is important to clarify what exactly you are trying to calculate. Are you looking for the total number of alpha particles scattered at angles greater than 60 degrees, or the number of alpha particles scattered at a specific angle greater than 60 degrees? The formula you have provided calculates the differential cross section for scattering at a specific angle, so you would need to integrate it over the solid angle to obtain the total number of particles scattered at that angle.

To answer your specific questions:

1) Your formula is not quite correct. The formula for the differential cross section for Rutherford scattering at a specific angle θ is given by:

dσ/dΩ = (Z^2e^4)/(16πε^2E^2sin^4(θ/2))

Where E is the kinetic energy of the alpha particles. So your formula should be:

dN/N = n*dσ/dΩ*dΩ

2) Yes, you would need to integrate the solid angle element from 60 to 360 degrees in order to obtain the total number of particles scattered at angles greater than 60 degrees.

3) The sin^4(θ/2) term is already included in the formula for the differential cross section, so you do not need to integrate it separately.

Finally, it is important to note that the Rutherford scattering formula is only valid for small scattering angles. For larger scattering angles, other factors such as multiple scattering and the finite size of the target need to be taken into account. So if you are looking for the total number of particles scattered at angles greater than 60 degrees, you may need to use a more sophisticated model or experimental data to obtain an accurate result.