File:RutherfordHyperbolas.png
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RutherfordHyperbolas.png (395 × 226 pixels, file size: 27 KB, MIME type: image/png)
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[edit]DescriptionRutherfordHyperbolas.png |
English: Hyperbolic trajectories of alpha particles scattering from Au nucleus as described in Rutherford's 1911 paper. |
Date | |
Source | Own work |
Author | Johnjbarton |
PNG development InfoField | This plot was created with Matplotlib. |
Source code InfoField | Python code# Code to create example hyperbolic trajectories for Rutherford scattering.
%matplotlib notebook
import numpy as np
import math
import matplotlib.pyplot as plot
import matplotlib.patches as mpatches
from IPython.display import HTML
# r(phi) = 2(p/b)^2/(e cos(phi) - 1)
# Where p is the impact parameter
# b is the closest approach radius
# and e = Sqrt((2p/b)^2 + 1)
# Units of "b", so r/b, p/b.
# b = 34fm
# Rutherford's table uses
# p/b = 10, 5, 2, 1, 0.5, 0.25, 0.125
def trajectory(p2b):
"""Array of r, theta describing hyperbolic trajectory fo p/b"""
p2bSq = p2b*p2b
e = np.sqrt(4* p2bSq + 1)
# Rutherford says "the eccentricity is sec theta"
# Reduce a bit to avoid very large r
phi_in = np.arccos(1/e) - 0.001
phi_out = -phi_in
phis = np.linspace(phi_in, phi_out, 50)
r2bs = [2 * p2bSq / (e * np.cos(phi) - 1) for phi in phis]
# Rotate to make the alpha particle come in from left side.
phi_lefts = [phi - phi_in + math.pi for phi in phis]
return (r2bs, phi_lefts)
def nucleus(r):
"""Array of r, theta describing a circle of radius r"""
phis = np.linspace(0, 2*math.pi, 50)
rs = [r for phi in phis]
return (rs, phis)
fig, ax = plot.subplots(subplot_kw={'projection': 'polar'})
r_max = 10
p2bs = [5, 2, 1, .5, .25, .125]
for p2b in p2bs:
r, t = trajectory(p2b)
display(f'p/b {p2b} angle {round(math.degrees(t[-1]))}')
ax.plot(t, r)
# 7.3fm Modern Au radius / 34fm Rutherford r_min = b
r, t = nucleus(7.3/34)
ax.plot(t,r,color='gray', fillstyle='full')
ax.set_rmax(r_max)
ax.set_axis_off()
plot.show()
plot.savefig('RutherfordHyperbolasRaw.png')
|
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[edit]I, the copyright holder of this work, hereby publish it under the following license:
This file is licensed under the Creative Commons Attribution 4.0 International license.
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 04:20, 22 June 2024 | 395 × 226 (27 KB) | Johnjbarton (talk | contribs) | Shrink canvas to crop it seems. | |
03:47, 22 June 2024 | 960 × 720 (32 KB) | Johnjbarton (talk | contribs) | Uploaded own work with UploadWizard |
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