Nuclear physics - ruthford scattering

[shahar weiss]

Homework Statement

Calculate the rate alpha particles reaches a detector in a ruthford scattering given the following data:
Kinetic energy of particles: 10Mev
rate of hitting the target: 10^6 particles/second
target is thin lead foil 1mm thick and has the density of 11.3 g/second
the detector is at 1 metter away from target with cross section area of 1 cm^2
with an angle of 90 degress with respect to the direction of the alpha sheaf

Homework Equations

1) d$$\sigma$$/d$$\Omega$$ ($$\theta$$) (meanning the differencial cross section with respect to theta) = (Z*Z'*e^2/4E)^2 * COSEC^4(THETA/2)

2) A0*$$\rho$$*t/A

3) dn(theta) = A0*$$\rho$$*t/A * incidennt flux * d$$\sigma$$/d$$\Omega$$ *d$$\Omega$$

The Attempt at a Solution

putting all the info in the equations i get that
dn = 1.6284*10^3 * cosec^4(theta/2) * d(omega) .
i just can't think of how to advance from here. i would be very happy for advice.
thank you in advance

 

[mark726]

Thank you for your post. To calculate the rate of alpha particles reaching a detector in a Rutherford scattering, we need to use the equations you have provided and some additional information.

First, we need to calculate the total number of alpha particles that are incident on the target per second. This can be done by multiplying the rate of hitting the target (10^6 particles/second) by the cross-sectional area of the target (1 cm^2). This gives us a total incident flux of 10^6 particles/cm^2 per second.

Next, we need to calculate the differential cross section with respect to theta, using the first equation you have provided. This equation takes into account the charge of the alpha particles (Z and Z'), the energy of the particles (E), and the scattering angle (theta). We can plug in the values given in the problem to get the differential cross section.

Now, we can use the second equation to calculate the number of scattered particles per unit solid angle (dn) at a specific scattering angle (theta). This equation takes into account the number of incident particles (A0), the density of the target (rho), the thickness of the target (t), and the cross-sectional area of the detector (A). We can plug in the values given in the problem, along with the incident flux and differential cross section we have calculated, to get a value for dn.

Finally, we can use the third equation to calculate the total rate of alpha particles reaching the detector at a specific scattering angle (theta). This equation takes into account the number of scattered particles per unit solid angle (dn), the incident flux, and the differential cross section. We can integrate this equation over all solid angles to get the total rate of alpha particles reaching the detector.

I hope this helps guide you in solving the problem. Let me know if you have any further questions.