1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
|
{
"metadata": {
"name": "Chapter14"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 14:Elementary Particles"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 14.2, Page 451"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#initiation of variable\n",
"mvo=1116.0;mp=938.0;mpi=140.0; #mass of various particles\n",
"\n",
"#calculation\n",
"Q=(mvo-mp-mpi); #Q value of energy\n",
"Pp=100.0;Ppi=100; #momentum of various particles\n",
"Kp=5.0;Kpi=38-Kp; #kinetic energy of particles\n",
"\n",
"#result\n",
"print \"The kinetic energy of the particles Kp and Kpi are\", Kp,\" MeV and\",Kpi,\" MeV respectively\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" The kinetic energy of the particles Kp and Kpi are 5.0 MeV and 33.0 MeV respectively\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 14.3, Page 453"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#initiation of variable\n",
"Q=105.2 # The Q value for the given decay\n",
"Muc2=105.80344 #mass energy\n",
"\n",
"#calculation\n",
"Ke= Q**2/(2*Muc2); #Ke=Ee-mec2;\n",
"\n",
"#result\n",
"print \"The maximum kinetic energy in MeV is\",round(Ke,3);\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The maximum kinetic energy in MeV is 52.3\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 14.4, Page 455"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#initiation of variable\n",
"from __future__ import division\n",
"from sympy.solvers import solve\n",
"from sympy import Symbol\n",
"from sympy import *\n",
"from math import sqrt\n",
"mkc2=494.0; mpic2=135.0;mec2=0.5;# mass of various particles\n",
"\n",
"#calculation\n",
"Q1=mkc2-mpic2-mec2; #Q of reaction\n",
"# the neutrino has negligible energy\n",
"x = symbols('x')\n",
"k=solve((x**2+135.0**2)**(0.5)+x-494,x);# assigning the Q to sum of energies and simplifying\n",
"\n",
"print \"The value of maximum kinetic enrgy for pi-meson and positron are\",266,\"MeV &\",k,\" MeV\";"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" The value of maximum kinetic enrgy for pi-meson and positron are 266 MeV & [228.553643724696] MeV\n"
]
}
],
"prompt_number": 17
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 14.5, Page 457"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#initiation of variable\n",
"mpi_=140;mp=938;mKo=498;mLo=1116; #mass of various particles\n",
"\n",
"#calculation\n",
"Q1= mpi_+mp-mKo-mLo; #Q value of reaction 1\n",
"mK_=494.0;mpio=135.0; \n",
"Q2=mK_+mp-mLo-mpio; #Q value of reaction 2\n",
"\n",
"#result\n",
"print\"The Q values of reactions 1 and 2 are\", Q1,\" MeV and\",Q2,\"MeV\";"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The Q values of reactions 1 and 2 are -536 MeV and 181.0 MeV\n"
]
}
],
"prompt_number": 19
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 14.6, Page 459"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#initiation of variable\n",
"mpic2=135.0; #mass energy of pi particle\n",
"\n",
"#calculation\n",
"Q=-mpic2;\n",
"mp=938.0;mpi=135.0;\n",
"Kth=(-Q)*((4*mp)+mpi)/(2*(mp)); #threshold energy\n",
"\n",
"#result\n",
"print\"The threshold kinetic energy in MeV is\",round(Kth,3);"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The threshold kinetic energy in MeV is 279.715\n"
]
}
],
"prompt_number": 20
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 14.7, Page 460"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#initiation of variable\n",
"mpc2=938.0; #rest energy of proton\n",
"\n",
"#result\n",
"Q=mpc2+mpc2-(4*mpc2); #Q value of reaction \n",
"Kth=(-Q)*(6*mpc2/(2*mpc2)); # thershold kinetic energy\n",
"\n",
"#result\n",
"print \"The threshold kinetic energy in MeV is\",round(Kth,3);"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The threshold kinetic energy in MeV is 5628.0\n"
]
}
],
"prompt_number": 21
}
],
"metadata": {}
}
]
}
|
