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Nicolas Mantilla Molina
TrabajosPregrado
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b64ddae2
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b64ddae2
authored
7 months ago
by
Nicolas Mantilla Molina
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semi empirical mass
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AtomicPhysics/EmpiricalMass.ipynb
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b64ddae2
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Formula de Masa Semi Empírica (Semi-Empirical Mass Formula - SEMF)"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"# Importamos las librerias necesarias\n",
"import numpy as np\n",
"import pandas as pd\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"# Definimos constantes\n",
"e = 1.602e-19 # Carga del electrón en Coulombs\n",
"mn = 1.675e-27 # Masa del neutrón en kg\n",
"mp = 1.673e-27 # Masa del protón en kg\n",
"c = 3.0e8 # Velocidad de la luz en m/s\n",
"a_v = 15.56e6*e # J\n",
"a_s = 17.23e6*e # J\n",
"a_c = 0.7e6*e # J\n",
"a_a = 23.28e6*e # J\n",
"a_p = 12.0e6*e # J\n",
"\n",
"# Hacemos una función para la masa semiempirica\n",
"def SEMF(Z, A):\n",
" # Verificamos la paridad\n",
" d = 1\n",
" if A%2 != 0:\n",
" d = 0\n",
" elif (A-Z)%2 != 0:\n",
" d = -1\n",
"\n",
" # Calculamos la energía de enlace\n",
" B = a_v*A - a_s*A**(2/3) - a_c*Z**2/A**(1/3) - a_a*(A-2*Z)**2/A + d*a_p/A**(1/2)\n",
"\n",
" # Devolvemos la masa y la energía de enlace\n",
" return [Z*mp + (A-Z)*mn - B/c**2, B]\n",
"\n",
"# Hacemos una función para el Z donde la masa es mínima\n",
"def Zmin(A):\n",
" return round((mn - mp + 4*a_a/c**2)/(2*a_c/(c**2*A**(1/3)) + 8*a_a/c**2/A))"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Para A = 16 el valor de Z es 8\n",
"Para A = 121 el valor de Z es 52\n",
"Para A = 122 el valor de Z es 52\n",
"Para A = 208 el valor de Z es 83\n"
]
}
],
"source": [
"# Calculamos los valores minimos de Z para A = 16, 121, 122 y 208\n",
"A = [16, 121, 122, 208]\n",
"Z = [Zmin(a) for a in A]\n",
"\n",
"# Imprimimos los valores\n",
"for i in range(4):\n",
" print(f\"Para A = {A[i]} el valor de Z es {Z[i]}\")"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "base",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.9.18"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
%% Cell type:markdown id: tags:
# Formula de Masa Semi Empírica (Semi-Empirical Mass Formula - SEMF)
%% Cell type:code id: tags:
```
python
# Importamos las librerias necesarias
import
numpy
as
np
import
pandas
as
pd
import
matplotlib.pyplot
as
plt
```
%% Cell type:code id: tags:
```
python
# Definimos constantes
e
=
1.602e-19
# Carga del electrón en Coulombs
mn
=
1.675e-27
# Masa del neutrón en kg
mp
=
1.673e-27
# Masa del protón en kg
c
=
3.0e8
# Velocidad de la luz en m/s
a_v
=
15.56e6
*
e
# J
a_s
=
17.23e6
*
e
# J
a_c
=
0.7e6
*
e
# J
a_a
=
23.28e6
*
e
# J
a_p
=
12.0e6
*
e
# J
# Hacemos una función para la masa semiempirica
def
SEMF
(
Z
,
A
):
# Verificamos la paridad
d
=
1
if
A
%
2
!=
0
:
d
=
0
elif
(
A
-
Z
)
%
2
!=
0
:
d
=
-
1
# Calculamos la energía de enlace
B
=
a_v
*
A
-
a_s
*
A
**
(
2
/
3
)
-
a_c
*
Z
**
2
/
A
**
(
1
/
3
)
-
a_a
*
(
A
-
2
*
Z
)
**
2
/
A
+
d
*
a_p
/
A
**
(
1
/
2
)
# Devolvemos la masa y la energía de enlace
return
[
Z
*
mp
+
(
A
-
Z
)
*
mn
-
B
/
c
**
2
,
B
]
# Hacemos una función para el Z donde la masa es mínima
def
Zmin
(
A
):
return
round
((
mn
-
mp
+
4
*
a_a
/
c
**
2
)
/
(
2
*
a_c
/
(
c
**
2
*
A
**
(
1
/
3
))
+
8
*
a_a
/
c
**
2
/
A
))
```
%% Cell type:code id: tags:
```
python
# Calculamos los valores minimos de Z para A = 16, 121, 122 y 208
A
=
[
16
,
121
,
122
,
208
]
Z
=
[
Zmin
(
a
)
for
a
in
A
]
# Imprimimos los valores
for
i
in
range
(
4
):
print
(
f
"
Para A =
{
A
[
i
]
}
el valor de Z es
{
Z
[
i
]
}
"
)
```
%% Output
Para A = 16 el valor de Z es 8
Para A = 121 el valor de Z es 52
Para A = 122 el valor de Z es 52
Para A = 208 el valor de Z es 83
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