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VPython program to simulate scattering of alpha particles off gold atoms.
from __future__ import division
from visual import *
from visual.graph import *
from math import *
size=1e-15
size2=1e-10
b=0.005*size2
start=100*size2
k=9e9
e=1.6e-19
alpha=sphere(pos=(-start,b,0),radius=0.1*size,color=color.red)
alpha.mass=4*1.67e-27
alpha.charge=+2*e
alpha.size=1e-12
alpha.energy=4e6*1.6e-19
alpha.speed=sqrt(2*alpha.energy/alpha.mass)
gold=sphere(pos=(0,0,0), radius=size, color=color.yellow)
gold.mass=197*1.67e-27
gold.charge=+79*e
shell=sphere(pos=gold.pos, radius=size2, color=color.green)
shell.mass=gold.mass/1837
shell.charge=-gold.charge
alpha.momentum=alpha.mass*alpha.speed*vector(1,0,0)
gold.momentum=gold.mass*vector(0,0,0)
alpha.trail=curve(color=alpha.color)
alpha.trail.append(pos=alpha.pos)
gold.trail=curve(color=gold.color)
gold.trail.append(pos=gold.pos)
r=alpha.pos-gold.pos
rhat=r/r.mag
r_min=r.mag
init_r=alpha.pos.mag
print(r,rhat,r.mag2)
dt=0.01*r.mag/alpha.speed
t=0
while alpha.pos.mag<2*init_r:
if r.mag>size:
F_alpha=k*alpha.charge*gold.charge*rhat/r.mag2
F_gold=-F_alpha
else:
F_alpha=k*alpha.charge*gold.charge*rhat*(r.mag/size)/(size*size)
F_gold=-F_alpha
if r.mag>size2:
F_alpha=F_alpha+k*alpha.charge*shell.charge*rhat/r.mag2
F_gold=-F_alpha
check=F_alpha+F_gold
#print(F_alpha.y)
alpha.momentum=alpha.momentum+F_alpha*dt
gold.momentum=gold.momentum+F_gold*dt
alpha.pos=alpha.pos+(alpha.momentum/alpha.mass)*dt
alpha.trail.append(pos=alpha.pos)
gold.pos=gold.pos+(gold.momentum/gold.mass)*dt
shell.pos=gold.pos
gold.trail.append(pos=gold.pos)
r=alpha.pos-gold.pos
rhat=r/r.mag
alpha.speed=alpha.momentum.mag/alpha.mass
dt=0.01*r.mag/alpha.speed
if r.mag<r_min:
r_min=r.mag
t=t+dt
if alpha.pos.x>0:
angle=degrees(atan(abs((alpha.pos.y-b)/alpha.pos.x)))
else:
angle=180-degrees(atan(abs((alpha.pos.y-b)/alpha.pos.x)))
print(b,alpha.pos.y/b,angle)
print(r.mag/size,r_min/size,r_min/size2)
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