{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\"Open            \"Open" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Energetics of nuclear reactions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This notebook is about the energy involved in nuclear processes. We take a look at\n", "1. Binding energy\n", "2. Alpha decay" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import pandas as pd\n", "pd.set_option('precision', 10)\n", "\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Binding energy" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Binding energy is the characteristic energy that is tied up in a nucleus to hold it together. When a nucleus forms, the required binding energy is taken from the mass of the constituents. As a result, the bound nucleus is lighter than the sum of constituents by an amount of mass corresponding to the binding energy of that nucleus. These conversions between energy and mass are rooted in the [mass-energy-equivalence](https://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence) and we will jump back and forth between mass and energy a lot more further down in this notebook.\n", "\n", "There are many places where you can find data about the binding energy for different nuclei - we will look at two of them." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### PNPI - [Petersburg Nuclear Physics Institute](http://dbserv.pnpi.spb.ru/)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A PDF of the binding energy data can be found [here](http://dbserv.pnpi.spb.ru/elbib/tablisot/toi98/www/astro/table2.pdf). We have reformatted the data into a csv file to make it easier to analyse." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# source data http://dbserv.pnpi.spb.ru/elbib/tablisot/toi98/www/astro/table2.pdf\n", "pnpi = pd.read_csv(\"./data/binding-energies-pnpi.csv\",header=7)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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AELBE (MeV)
01H0.0000
12H2.2245
23H8.4820
33He7.7186
44He28.2970
\n", "
" ], "text/plain": [ " A EL BE (MeV)\n", "0 1 H 0.0000\n", "1 2 H 2.2245\n", "2 3 H 8.4820\n", "3 3 He 7.7186\n", "4 4 He 28.2970" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pnpi.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The PNPI data above contains the following columns of data:\n", "- **A** - Atomic mass number\n", "- **EL** - Element label\n", "- **BE (MeV)** - Binding energy in MeV" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is instructive to calculate the binding energy per nucleon - this gives us a sense of which nuclei are particularly stable." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "pnpi[\"BE/A (MeV)\"] = pnpi[\"BE (MeV)\"]/pnpi[\"A\"]" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pnpi.plot.scatter(x=\"A\", y=\"BE/A (MeV)\",figsize=(15,8), title=\"Binding energy per nucleon (Fig 1)\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The most stable element is the one with maximum binding energy per nucleon - it is Ni-62" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "A 62\n", "EL Ni\n", "BE (MeV) 545.2682\n", "BE/A (MeV) 8.794648387\n", "Name: 371, dtype: object" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "most_stable_index = pnpi[\"BE/A (MeV)\"].argmax()\n", "pnpi.loc[most_stable_index]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The hump shape of Fig 1 indicates that energy can be released from nuclear fusion of light elements and nuclear fission of heavy elements. \n", "\n", "The current data only goes up to atomic mass 135. To go further we need to look at a different dataset" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### IAEA nuclear data services - [Atomic Mass Data Center](https://www-nds.iaea.org/amdc/)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A txt file containing the binding energy data can be found [here](https://www-nds.iaea.org/amdc/ame2016/mass16.txt). We have reformatted the data into a csv file to make it easier to analyse and excluded non-experimental values (denoted by # in the original txt file)." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "# source data https://www-nds.iaea.org/amdc/ame2016/mass16.txt\n", "iaea = pd.read_csv(\"./data/binding-energies-iaea.csv\",header=13)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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NZAELDEL_M (keV)BE/A (keV)Mass (mu-u)
0101n8071.317130.0001.0086649160e+06
1011H7288.970610.0001.0078250320e+06
2112H13135.721761112.2832.0141017780e+06
3213H14949.809932827.2653.0160492820e+06
4123He14931.217932572.6803.0160293230e+06
\n", "
" ], "text/plain": [ " N Z A EL DEL_M (keV) BE/A (keV) Mass (mu-u)\n", "0 1 0 1 n 8071.31713 0.000 1.0086649160e+06\n", "1 0 1 1 H 7288.97061 0.000 1.0078250320e+06\n", "2 1 1 2 H 13135.72176 1112.283 2.0141017780e+06\n", "3 2 1 3 H 14949.80993 2827.265 3.0160492820e+06\n", "4 1 2 3 He 14931.21793 2572.680 3.0160293230e+06" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "iaea.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The IAEA data above contains the following columns of data:\n", "- **N** - Number of neutrons\n", "- **Z** - Number of protons\n", "- **A** - Atomic mass number\n", "- **EL** - Element label\n", "- **DEL_M (keV)** - [Mass excess](https://en.wikipedia.org/wiki/Mass_excess) in keV (technically this should be $keV/c^2$ but the $c^2$ factor is often dropped)\n", "- **BE/A (keV)** - Binding energy per nucleon in keV\n", "- **Mass (mu-u)** - Atomic mass in millionths of a standard [atomic mass unit](https://en.wikipedia.org/wiki/Dalton_(unit%29) (aka Dalton)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's first renormalise our units from `keV` into `MeV` for energy and from `mu-u` to `u` for mass units. (*n.b. we don't do this in the csv file because of the [precision limitations](https://docs.python.org/3/tutorial/floatingpoint.html) of the resulting floating point numbers*)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "iaea[\"BE/A (keV)\"] = iaea[\"BE/A (keV)\"]/1000\n", "iaea[\"DEL_M (keV)\"] = iaea[\"DEL_M (keV)\"]/1000\n", "iaea[\"Mass (mu-u)\"] = iaea[\"Mass (mu-u)\"]/1000000\n", "iaea.rename(columns={'BE/A (keV)': 'BE/A (MeV)', 'DEL_M (keV)': 'DEL_M (MeV)', 'Mass (mu-u)': 'Mass (u)'}, inplace=True)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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NZAELDEL_M (MeV)BE/A (MeV)Mass (u)
0101n8.071317130.0000001.008664916
1011H7.288970610.0000001.007825032
2112H13.135721761.1122832.014101778
3213H14.949809932.8272653.016049282
4123He14.931217932.5726803.016029323
\n", "
" ], "text/plain": [ " N Z A EL DEL_M (MeV) BE/A (MeV) Mass (u)\n", "0 1 0 1 n 8.07131713 0.000000 1.008664916\n", "1 0 1 1 H 7.28897061 0.000000 1.007825032\n", "2 1 1 2 H 13.13572176 1.112283 2.014101778\n", "3 2 1 3 H 14.94980993 2.827265 3.016049282\n", "4 1 2 3 He 14.93121793 2.572680 3.016029323" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "iaea.head()" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "iaea.plot.scatter(x=\"A\", y=\"BE/A (MeV)\",figsize=(15,8), title=\"Binding energy per nucleon (Fig 2)\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Fig 2 is much more similar to what we see in text books at school. \n", "\n", "We can also check to see whether the IAEA data agrees with PNPI about the most stable element." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "N 34\n", "Z 28\n", "A 62\n", "EL Ni\n", "DEL_M (MeV) -66.746323\n", "BE/A (MeV) 8.794553\n", "Mass (u) 61.92834487\n", "Name: 441, dtype: object" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "most_stable_index = iaea[\"BE/A (MeV)\"].argmax()\n", "iaea.loc[most_stable_index]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Ni-62 again - lovely.\n", "\n", "We are now going to use the IAEA data to look at the energetics of alpha decay." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Alpha decay" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### What is an alpha particle?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[Alpha decay](https://en.wikipedia.org/wiki/Alpha_decay) is a process that involves an unstable parent nucleus \"spitting out\" a He-4 nucleus (aka an alpha particle). Let's have a look at the alpha particle and see if we can understand the iaea data for it.\n", "\n", "To extract only the alpha particle entry (with N=2 and Z=2) from the iaea table, we can use the [`query`](https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.DataFrame.query.html) function from pandas" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
NZAELDEL_M (MeV)BE/A (MeV)Mass (u)
6224He2.424915617.0739154.002603254
\n", "
" ], "text/plain": [ " N Z A EL DEL_M (MeV) BE/A (MeV) Mass (u)\n", "6 2 2 4 He 2.42491561 7.073915 4.002603254" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "alpha = iaea.query(\"N==2 & Z==2\")\n", "alpha" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Although `DEL_M (MeV)`, `BE/A (MeV)` and `Mass (u)` might appear like independent quantities, they are in fact intimately related to each other, let's see how." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Mass is the most familiar to us so we'll start there. We normally think of helium as having a mass of 4, associated with the number of nucleons from which it is made (2 protons and 2 neutrons), but this simple picture is not the whole story. \n", "\n", "In [atomic mass units](https://en.wikipedia.org/wiki/Dalton_(unit%29) `u` (aka Dalton), The mass of helium in is 4.002603254.\n", "\n", "Compare this with the mass of 2 protons and 2 neutrons:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "proton = iaea.query(\"N==0 & Z==1\")\n", "neutron = iaea.query(\"N==1 & Z==0\")" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "4.0329798960000005" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "2*proton[\"Mass (u)\"].values[0] + 2*neutron[\"Mass (u)\"].values[0]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There is a difference between the two values (a [mass defect](https://en.wikipedia.org/wiki/Nuclear_binding_energy#Mass_defect)), the mass of helium is less than the mass of its constituent protons by an amount:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.03037664200000023" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mass_defect = 4.0329798960000005 - 4.002603254\n", "mass_defect" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "or, energy units $1u = 931.494MeV$," ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "u = 931.494" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "28.295659763148215" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mass_defect*u" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This 28.2957MeV is the energy needed to split the helium apart into its protons and neutrons, i.e. this is the binding energy. Per nucleon this is exactly what appears in the `BE/A (MeV)` column of the iaea table." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "7.073914940787054" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "alpha_binding_energy = mass_defect*u/4\n", "alpha_binding_energy" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is sometimes convenient to think about the mass of a nucleus in terms of how much it deviates from the simple picture given by the number of nucleons. For Heluium this would be:" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.002603254000000277" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "4.002603254 - 4" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "or, energy units," ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.424915481476258" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(4.002603254 - 4)*u" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This 2.4249MeV is called Mass excess and is what appears in the in the `DEL_M (MeV)` column of the iaea table." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Spontaneous alpha decay " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Alpha decay creates a daughter nucleus with 2 fewer protons and 2 fewer neutrons than the parent. \n", "\n", "Let's look at a real life example. The alpha decay of [uranium-238](https://en.wikipedia.org/wiki/Uranium-238)." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
NZAELDEL_M (MeV)BE/A (MeV)Mass (u)
239514692238U47.3077837.570125238.050787
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" ], "text/plain": [ " N Z A EL DEL_M (MeV) BE/A (MeV) Mass (u)\n", "2395 146 92 238 U 47.307783 7.570125 238.050787" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "U238 = iaea.query(\"N==146 & Z==92\")\n", "U238" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Subtracting the alpha nucleus from the U-238 gives us an element with the following number of neutrons and protons:" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
NZ
239514490
\n", "
" ], "text/plain": [ " N Z\n", "2395 144 90" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "daughter_NZ = U238[[\"N\",\"Z\"]] - alpha[[\"N\",\"Z\"]].values[0]\n", "daughter_NZ" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "What is this element? We need to query the iaea table." ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
NZAELDEL_M (MeV)BE/A (MeV)Mass (u)
236714490234Th40.6130097.596855234.0435999
\n", "
" ], "text/plain": [ " N Z A EL DEL_M (MeV) BE/A (MeV) Mass (u)\n", "2367 144 90 234 Th 40.613009 7.596855 234.0435999" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Th234 = iaea.query(\"N==144 & Z==90\")\n", "Th234" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The alpha decay product of uranium-238 is apparently thorium-234. This decay can (and indeed does) happen spontaneously in nature because of the positive mass difference between the U-238 and the products (Th-234 +alpha). Let's see this explicitly:" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.004583846000002723" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mass_defect = U238[\"Mass (u)\"].values[0] - (Th234[\"Mass (u)\"].values[0] + alpha[\"Mass (u)\"].values[0])\n", "mass_defect" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "U-238 has more mass than the Th-234 + alpha. This mass difference is converted to kinetic energy of the products (with most going to the alpha because it's much lighter than Th).\n", "\n", "We can therefore expect that the alpha particle will be released with the following kinetic energy (in MeV):" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "4.269825045926536" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mass_defect*u" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is indeed what is reported (see \"Decay modes\" in [U-238 wiki entry](https://en.wikipedia.org/wiki/Uranium-238))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Induced alpha decay" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In addition to decay processes that happen spontaneously, we can also imagine exciting nuclei into higher energy states from which they are then energetically able to decay. [Photodisintegration](https://en.wikipedia.org/wiki/Photodisintegration), [Photofission](https://en.wikipedia.org/wiki/Photofission) and [Neutron activation](https://en.wikipedia.org/wiki/Neutron_activation) are examples of such a situation.\n", "\n", "Another important example (in the context of nuclear fusion) that we'll now look at is the [breeding of tritium from lithium](https://en.wikipedia.org/wiki/Tritium#Lithium)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Most of the lithium in the world is Li-7" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
NZAELDEL_M (MeV)BE/A (MeV)Mass (u)
16437Li14.907105295.6064397.016003437
\n", "
" ], "text/plain": [ " N Z A EL DEL_M (MeV) BE/A (MeV) Mass (u)\n", "16 4 3 7 Li 14.90710529 5.606439 7.016003437" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Li7 = iaea.query(\"N==4 & Z==3\")\n", "Li7" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we are to imagine the possibility of Li-7 undergoing alpha decay, then it's daughter nucleus would have the following number of neutrons and protons:" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
NZ
1621
\n", "
" ], "text/plain": [ " N Z\n", "16 2 1" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "daughter_NZ = Li7[[\"N\",\"Z\"]] - alpha[[\"N\",\"Z\"]].values[0]\n", "daughter_NZ" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This daughter element is H-3, otherwise knows as tritium" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
NZAELDEL_M (MeV)BE/A (MeV)Mass (u)
3213H14.949809932.8272653.016049282
\n", "
" ], "text/plain": [ " N Z A EL DEL_M (MeV) BE/A (MeV) Mass (u)\n", "3 2 1 3 H 14.94980993 2.827265 3.016049282" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "H3 = iaea.query(\"N==2 & Z==1\")\n", "H3" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "However, if we look at the difference in energy (in MeV) between Li-7 and products (i.e H-3 + alpha):" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-2.4676198239044376" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(Li7[\"Mass (u)\"].values[0] - (H3[\"Mass (u)\"].values[0] + alpha[\"Mass (u)\"].values[0]))*u" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that it's negative i.e. spontaneous decay is not energetically possible.\n", "\n", "We can however create an excited form of Li-7 by \"bombarding\" Li-6 with neutrons." ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
NZAELDEL_M (MeV)BE/A (MeV)Mass (u)
13336Li14.086878955.3323316.015122887
\n", "
" ], "text/plain": [ " N Z A EL DEL_M (MeV) BE/A (MeV) Mass (u)\n", "13 3 3 6 Li 14.08687895 5.332331 6.015122887" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Li6 = iaea.query(\"N==3 & Z==3\")\n", "Li6" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The energy difference between reactants (Li-6 + n) and products (H-3 + alpha) is then:" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "4.783470398898826" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "( Li6[\"Mass (u)\"].values[0] + neutron[\"Mass (u)\"].values[0] - \n", " (H3[\"Mass (u)\"].values[0] + alpha[\"Mass (u)\"].values[0]) )*u" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So, 4.78MeV of energy is released via alpha decay when we combine Li-6 with a neutron - there is therefore no need to \"bombard\" the Li-6 with very high energy neutrons, apparently any energy will do.\n", "\n", "We can play these kind of energy comparison games for many different scenarios in order to hunt for possible novel reactions. It is helpful to be able to do these comparisons across many elements at once - this is what we will finish with." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Automation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We are now going to extend some of the code used when looking at the alpha decay of an individual nucleus. This will allow us to analyse all the elements in one go. In a sense we will be gathering together many hypothetical reactions from which we can later select/discard according to energy conservation criteria." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We start as we did before by subtracting the alpha nucleus, but this time from **all** elements in the iaea list. This gives us daughter nuclei with the following number of neutrons and protons:" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [], "source": [ "daughter_NZ = iaea[[\"N\",\"Z\"]] - alpha[[\"N\",\"Z\"]].values[0]" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
NZ
0-1-2
1-2-1
2-1-1
30-1
4-10
51-1
600
7-11
82-1
910
\n", "
" ], "text/plain": [ " N Z\n", "0 -1 -2\n", "1 -2 -1\n", "2 -1 -1\n", "3 0 -1\n", "4 -1 0\n", "5 1 -1\n", "6 0 0\n", "7 -1 1\n", "8 2 -1\n", "9 1 0" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "daughter_NZ.head(10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Some of the rows in the above table don't make sense because they are either both zero or contain negative numbers. The first row that does make sense is row number 9.\n", "\n", "Although we can tell by eye that the daughter element corresponding the row 9 with N=1 and Z=0 is the neutron, in general we will need to query the iaea table to find this out. This querying is similar to what we did earlier, the only difference is that below we now use [fstrings](https://realpython.com/python-f-strings/) to demonstrate how we go about removing the hard coded numbers." ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'N==1 & Z==0'" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "q = f\"N=={daughter_NZ.loc[9]['N']} & Z=={daughter_NZ.loc[9]['Z']}\"\n", "q" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
NZAELDEL_M (MeV)BE/A (MeV)Mass (u)
0101n8.071317130.01.008664916
\n", "
" ], "text/plain": [ " N Z A EL DEL_M (MeV) BE/A (MeV) Mass (u)\n", "0 1 0 1 n 8.07131713 0.0 1.008664916" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "iaea.query(q)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We are now ready to automate the process of finding the daughter elements (for those that have one)." ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [], "source": [ "parent_index = []\n", "daughter_index = []\n", "for i, row in daughter_NZ.iterrows():\n", " try:\n", " q = f\"N=={row['N']} & Z=={row['Z']}\"\n", " daughter_index.append(iaea.query(q).index[0])\n", " parent_index.append(i)\n", " except:\n", " continue" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [], "source": [ "parents_alpha_decay = iaea.loc[parent_index]\n", "parents_alpha_decay.reset_index(inplace=True, drop=True)\n", "\n", "daughters_alpha_decay = iaea.loc[daughter_index]\n", "daughters_alpha_decay.reset_index(inplace=True, drop=True)" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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NZAELDEL_M (MeV)BE/A (MeV)Mass (u)
0325He11.231233005.5121325.012057224
1235Li11.678886005.2661325.012537800
2336Li14.086878955.3323316.015122887
3437Li14.907105295.6064397.016003437
4347Be15.768999005.3715487.016928717
\n", "
" ], "text/plain": [ " N Z A EL DEL_M (MeV) BE/A (MeV) Mass (u)\n", "0 3 2 5 He 11.23123300 5.512132 5.012057224\n", "1 2 3 5 Li 11.67888600 5.266132 5.012537800\n", "2 3 3 6 Li 14.08687895 5.332331 6.015122887\n", "3 4 3 7 Li 14.90710529 5.606439 7.016003437\n", "4 3 4 7 Be 15.76899900 5.371548 7.016928717" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "parents_alpha_decay.head()" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
NZAELDEL_M (MeV)BE/A (MeV)Mass (u)
0101n8.071317130.0000001.008664916
1011H7.288970610.0000001.007825032
2112H13.135721761.1122832.014101778
3213H14.949809932.8272653.016049282
4123He14.931217932.5726803.016029323
\n", "
" ], "text/plain": [ " N Z A EL DEL_M (MeV) BE/A (MeV) Mass (u)\n", "0 1 0 1 n 8.07131713 0.000000 1.008664916\n", "1 0 1 1 H 7.28897061 0.000000 1.007825032\n", "2 1 1 2 H 13.13572176 1.112283 2.014101778\n", "3 2 1 3 H 14.94980993 2.827265 3.016049282\n", "4 1 2 3 He 14.93121793 2.572680 3.016029323" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "daughters_alpha_decay.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The above two tables pair the parents and daughters together. We can now calculate the kinetic energy of the hypothetical decay reactions." ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [], "source": [ "parents_alpha_decay[\"E_kin (MeV)\"] = (parents_alpha_decay[\"Mass (u)\"] - \n", " (daughters_alpha_decay[\"Mass (u)\"] + alpha[\"Mass (u)\"].values[0]))*u" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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NZAELDEL_M (MeV)BE/A (MeV)Mass (u)E_kin (MeV)
0325He11.231233005.5121325.0120572240.7349990667
1235Li11.678886005.2661325.0125378001.9649996339
2336Li14.086878955.3323316.015122887-1.4737585746
3437Li14.907105295.6064397.016003437-2.4676198239
4347Be15.768999005.3715487.016928717-1.5871353668
5538Li20.945804005.1597128.022486246-6.1002387007
6448Be4.941671007.0624358.0053051020.0918397194
7358B22.921567004.7171558.024607316-4.8265361610
8639Li24.954902005.0377689.026790191-10.3624571667
9549Be11.348453006.4626689.012183066-2.3076944135
\n", "
" ], "text/plain": [ " N Z A EL DEL_M (MeV) BE/A (MeV) Mass (u) E_kin (MeV)\n", "0 3 2 5 He 11.23123300 5.512132 5.012057224 0.7349990667\n", "1 2 3 5 Li 11.67888600 5.266132 5.012537800 1.9649996339\n", "2 3 3 6 Li 14.08687895 5.332331 6.015122887 -1.4737585746\n", "3 4 3 7 Li 14.90710529 5.606439 7.016003437 -2.4676198239\n", "4 3 4 7 Be 15.76899900 5.371548 7.016928717 -1.5871353668\n", "5 5 3 8 Li 20.94580400 5.159712 8.022486246 -6.1002387007\n", "6 4 4 8 Be 4.94167100 7.062435 8.005305102 0.0918397194\n", "7 3 5 8 B 22.92156700 4.717155 8.024607316 -4.8265361610\n", "8 6 3 9 Li 24.95490200 5.037768 9.026790191 -10.3624571667\n", "9 5 4 9 Be 11.34845300 6.462668 9.012183066 -2.3076944135" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ "parents_alpha_decay.head(10)" ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "parents_alpha_decay.plot.scatter(x=\"A\", y=\"E_kin (MeV)\",figsize=(15,8), \n", " title=\"Kinetic energy of alpha decay products (Fig 3)\");\n", "plt.plot((270, 0), (0, 0), 'r-');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Fig 3 shows us that on the whole (with the exception of He-5, Li-5 and Be-8) spontaneous alpha decay is only energetically possible when the mass number gets higher than about 100. We can see this explicitly by querying the `parents_alpha_decay` table" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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NZAELDEL_M (MeV)BE/A (MeV)Mass (u)E_kin (MeV)
0325He11.2312335.5121325.0120572240.7349990667
1235Li11.6788865.2661325.0125378001.9649996339
6448Be4.9416717.0624358.0053051020.0918397194
7885250102Sn-64.9348848.324430101.9302895000.2765847875
8005350103Sn-66.9725918.341757102.9281020000.5336491866
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2330156108264Hs119.5632227.298375264.12835640010.5907570312
2331157108265Hs120.9002837.296247265.12979180010.4703148569
2332158108266Hs121.1363737.298273266.13004530010.3457741091
2333159110269Ds134.8347097.250154269.14475100011.5094895633
2334160110270Ds134.6782827.253775270.14458310011.1169579917
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1107 rows × 8 columns

\n", "
" ], "text/plain": [ " N Z A EL DEL_M (MeV) BE/A (MeV) Mass (u) E_kin (MeV)\n", "0 3 2 5 He 11.231233 5.512132 5.012057224 0.7349990667\n", "1 2 3 5 Li 11.678886 5.266132 5.012537800 1.9649996339\n", "6 4 4 8 Be 4.941671 7.062435 8.005305102 0.0918397194\n", "788 52 50 102 Sn -64.934884 8.324430 101.930289500 0.2765847875\n", "800 53 50 103 Sn -66.972591 8.341757 102.928102000 0.5336491866\n", "... ... ... ... .. ... ... ... ...\n", "2330 156 108 264 Hs 119.563222 7.298375 264.128356400 10.5907570312\n", "2331 157 108 265 Hs 120.900283 7.296247 265.129791800 10.4703148569\n", "2332 158 108 266 Hs 121.136373 7.298273 266.130045300 10.3457741091\n", "2333 159 110 269 Ds 134.834709 7.250154 269.144751000 11.5094895633\n", "2334 160 110 270 Ds 134.678282 7.253775 270.144583100 11.1169579917\n", "\n", "[1107 rows x 8 columns]" ] }, "execution_count": 44, "metadata": {}, "output_type": "execute_result" } ], "source": [ "parents_alpha_decay.query(\"`E_kin (MeV)` > 0\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also see that if we are able to deposit more energy (in MeV) than" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "25.474734511475653" ] }, "execution_count": 45, "metadata": {}, "output_type": "execute_result" } ], "source": [ "abs(parents_alpha_decay[\"E_kin (MeV)\"].min())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Then, energetically speaking, alpha decay is possible for all elements." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Some elements, require a lot less than 25MeV. For example, we can \"chain\" together the query function to the plotting function in order to conveniently pick out [Palladium](https://en.wikipedia.org/wiki/Palladium) and [Silver](https://en.wikipedia.org/wiki/Silver)" ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(nrows=1, ncols=2, figsize=(15,8), sharey=True)\n", "\n", "parents_alpha_decay.query(\"EL=='Pd'\").plot.scatter(x=\"A\", y=\"E_kin (MeV)\", ax=axes[0],\n", " title=\"Kinetic energy of Pd alpha decay products (Fig 4)\", label=\"Pd isotopes\");\n", "\n", "parents_alpha_decay.query(\"EL=='Ag'\").plot.scatter(x=\"A\", y=\"E_kin (MeV)\",ax=axes[1],\n", " title=\"Kinetic energy of Ag alpha decay products (Fig 5)\", label=\"Ag isotopes\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For the most abundant type of palladium (Pd-108):" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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NZAELDEL_M (MeV)BE/A (MeV)Mass (u)E_kin (MeV)
8546246108Pd-89.5242068.567023107.9038918-3.8534546799
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" ], "text/plain": [ " N Z A EL DEL_M (MeV) BE/A (MeV) Mass (u) E_kin (MeV)\n", "854 62 46 108 Pd -89.524206 8.567023 107.9038918 -3.8534546799" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" } ], "source": [ "parents_alpha_decay.query(\"EL=='Pd' & A==108\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We would need to provide at least 3.9MeV of energy to make alpha decay energetically possible.\n", "\n", "In contrast, Silver (whose most abundant isotope is Ag-107):" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
NZAELDEL_M (MeV)BE/A (MeV)Mass (u)E_kin (MeV)
8446047107Ag-88.406678.5539106.9050915-2.7999349659
\n", "
" ], "text/plain": [ " N Z A EL DEL_M (MeV) BE/A (MeV) Mass (u) E_kin (MeV)\n", "844 60 47 107 Ag -88.40667 8.5539 106.9050915 -2.7999349659" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" } ], "source": [ "parents_alpha_decay.query(\"EL=='Ag' & A==107\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "requires only 2.8MeV." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Next up...\n", "\n", "Energetics is just one of the factors to consider when hunting for possible novel nuclear reactions. We will explore some of the other factors in the next notebook." ] } ], "metadata": { "jupytext": { "formats": "ipynb,src//md" }, "kernelspec": { "display_name": "Python 3", "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": "3.7.1" } }, "nbformat": 4, "nbformat_minor": 4 }