Rutherford+Scattering

= Rutherford Scattering =

Author: Daniel Sinkovitz, 2011

Materials:
[|BouncingBall.zip]

Remember Ernest Rutherford’s famous gold foil experiment? He bombarded very thin gold foil with a beam of alpha particles and observed how they scattered. His surprising result led to a new understanding of atomic structure.

Today, we’ll simulate that experiment using your knowledge of electric forces, Newton’s laws, and molecular dynamics simulations (from the last time I was in). I’ll give you a partial source code, and you’ll complete it.

>> >>> >>>> i. Read into Excel using Data → From Text, and find myfile.txt. ii. Choose Fixed Width or Delineated by space.
 * 1) ** Download the source code: **
 * 2) Find the Rutherford folder on teacher_data/vondracek.
 * 3) Copy the whole folder to your network folder.
 * 4) Open it and open the Rutherford project file by double clicking on it.
 * 5) Read it through carefully to understand what it is doing. Ask any questions you may have.
 * 1) ** Fill in the missing constants: **
 * 2) Use Google or any source to find the constants to replace all the “???”.
 * 1) ** Complete the **** compute_accelerations **** function: **
 * 2) The gold nucleus is at the origin, and x, y are the coordinates of the alpha particle.
 * 3) Using this, calculate the force on the alpha particle.
 * 4) Break the force into x and y components. (Use a right triangle diagram.)
 * 5) Compute the new acceleration of the alpha particle and store it in ax, ay.
 * 1) ** Simulate varying impact factor: **
 * 2) ** Plot ** the x,y curve in Excel for velocity = 0.05//c// and impact parameter = 0.1 pm.

> > >> i. You’ll have to silence the part where it asks you what impact factor to use.
 * 1) On the same plot, **add curves** for impact parameter 0.2 pm and 0.05 pm.
 * 2) How does the curve depend on impact parameter? Explain this.
 * 1) ** Varying alpha particle velocity: **
 * 2) ** Plot ** the x,y curves in Excel for impact parameter 0.05 pm and velocities = 0.05//c//, 0.10//c//, and 0.15//c//.
 * 3) How does the curve depend on alpha particle initial velocity? Explain this.
 * 1) ** Plotting exit angle vs impact parameter. **
 * 2) Comment out the printing that occurs on each timestep.
 * 3) Just report at the end the impact factor and exit angle.
 * 4) Start the particles at x = −100 pm.
 * 5) Try a few velocities and impact parameters.
 * 6) Add a loop to search over a range of impact factors.

> > > Describe in detail how you could use this program to calculate the ratio between the number of particles that scatter between angles 0° and 90° and the number that scatter between 90° and 180°. > > > > > > > > > > > > > > >> What would be interesting to you? >> >> >> >> >>> >>> >>> >>> >>> >>>
 * 1) ** Plot ** the exit angle vs impact factor for velocity = 0.05//c// and for impact factors ranging from 0.00 to 1.00 pm.
 * 2) How does the exit angle vs impact factor curve inform you of the relative likelihood of scattering at a large angle vs a small angle? Explain clearly.
 * 1) Suppose you know that each impact parameter is equally likely.
 * 1) How does this procedure change if you know that, instead, an alpha particle is equally to strike within an area of large circular cross section? (M-V students, I expect a more detailed answer from you, with the actual math involved.)
 * 1) ** Thinking ahead: **
 * 2) After this activity, what other systems can you imagine simulating?
 * 1) ** Challenge: Adding recoil to the gold nucleus: **
 * 2) Before we assumed that the gold nucleus didn’t recoil, as if it had infinite mass.
 * 3) Look up the mass of a gold nucleus and add it in to the other constants.
 * 4) Add in coordinates of the gold nucleus. Use X, Y , VX , VY , AX , and AY.
 * 5) Have the calculate_accelerations function update AX and AY.
 * 6) Add in the code to move the gold nucleus with time just like the alpha particle.
 * 7) Compare the exit angle vs impact parameter curves with and without recoil. Does recoil make much of a difference? Why do you think this is?
 * 1) What could you try to find an increased difference between the two cases?
 * 1) Try it. What do you observe?