The following code is the skeleton of a computational model of a collision between a single moving alpha particle and a single gold nucleus which is initially stationary. Some pieces of the physical model are missing. An alpha particle consists of 2 protons and 2 neutrons. A gold nucleus contains 79 protons and 118 neutrons.

from visual import * 

from visual.graph import * 

scene.width = 1024 

scene.height = 600 

q_e = 1.6e19 

m_p = 1.7e27 

oofpez = 9e9 

m_Au = (79+118) * m_p 

m_Alpha = (2+2) * m_p 

qAu = 2 * q_e 

qAlpha = 79 * q_e 

deltat = 1e23 

Au = sphere(pos=vector(0,0,0), radius=4e15, 

 color=color.yellow, make_trail=True) 

Alpha = sphere(pos=vector(1e13,5e15,0), 

 radius=1e15, color=color.magenta, 

 make_trail=True) 

p_Au = m_Au*vector(0,0,0) 

p_Alpha = vector(1.043e19,0,0) 

t = 0 

while t<1.3e20: 

 rate(100) 

 Alpha.pos = Alpha.pos+(p_Alpha/m_Alpha) * 

deltat 

 t = t + deltat 

(a)

Read the code, and predict what will happen when the unmodified skeleton program is run. Then run the program to check your prediction.

(b)

Modify the program so that it represents a reasonable physical model of this interaction.

(c)

Does the gold nucleus move during these collisions? Should it? You can see the trail left by the gold nucleus better if you make this object slightly transparent by adding this line of code before the loop: Au.opacity = 0.7

(d)

What is the value of the impact parameter b in this program? Experiment with different impact parameters, and report what you observe.

(e)

After the loop, add to your program a calculation of the scattering angle (the angle between the final and initial momenta of the alpha particle). The VPython function for the dot product is dot(A,B). The function acos(D) returns the angle (in radians) whose cosine is D. Check to make sure the angle you calculate makes sense in terms of what you observe on the screen.

(f) Find values of the impact parameter that lead to the following scattering angles:

(1)90

(2)168

(3)38

(4)13.