(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Spray of alpha particles hit a gold membrane whose density is[itex]\rho[/itex]and thicknessd, with a kinetic energy of[itex]E_k[/itex]. The spray's intensity isI. Alpha particles are measured from an area ofAwhich is setRaway from the membrane. If[itex]\theta[/itex]is the angle between the spray hitting the membrane and the center of the areaA, what is the amount of alpha particles hitting the areaAin one hour when[itex]\theta[/itex]= 10 degrees.

2. Relevant equations

The propability equation for alpha particles going into an angle of[itex]\theta[/itex]after hitting the membrane.

[itex]\frac{d\sigma}{d\Omega}[/itex] = [itex](\frac{z*Z*e^2}{8*\pi*\epsilon*M*v^2})^2*\frac{1}{sin(\theta/2)^4}[/itex]

Wherez = alpha particle's charge, Z = gold's atomic number, M = alpha particle's mass and \epsilon = vacuum permittivity

[itex]\rho = 19.3(g/cm^3), M_{au} = 197u, Z_{au} = 79, d = 0.1*10^{-6}m, I = 10^4(Particles/Second), A = 1.0cm^2, R = 10cm[/itex]

3. The attempt at a solution

I would assume the straight forward way of doing this would be to calculate the probability for the particles to hit the angle and then multiply that with the intensity and then multiply that with 60s*60min to get the particles per one hour.

First i changed the equation to this form. ( z = 2e and i added 2*0.5 = 1 to the denominator)

[itex]\frac{d\sigma}{d\Omega}[/itex] = [itex](\frac{2e*79*e^2}{8*\pi*\epsilon*0.5*2*M*v^2})^2 * \frac{1}{sin(\theta/2)^4}[/itex]

Thus i can just throw in the kinetic energy to the denominator and make it look like

[itex]\frac{d\sigma}{d\Omega}[/itex] = [itex](\frac{79*e^3}{8*\pi*\epsilon*E_k})^2*\frac{1}{sin(\theta/2)^4}[/itex]

And after putting the numbers in i get [itex]\approx 5.1216 \dots * 10^{-62}[/itex]

That's most likely not correct. Anyone care to help?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Rutherford scattering differential probability function

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**