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Radioactive Decay Energy¶

Within the ejecta of a supernova, the gammarays largely come from the decay of \(^{56}Ni\) into \(^{56}Co\). This releases a large amount of energy. To understand how much energy is produced from this decay we look at the amount of energy 1 g of \(^{56}Ni\) produces in 10 days

The equation for radioactive decay is

\[N(t) = N_\mathrm{0} \exp\left(-\lambda t \right)\]

\(N(t)\) is the number of atoms after time t, \(N_\mathrm{0}\) is the initial number of atoms, and \(\lambda\) is the half life.

Using the molar mass, we find that 1g of \(^{56}Ni\) has \(1.0767e22\) atoms. The half life of \(^{56}Ni\) is 6.10 days. Plugging these numbers into the equation we can find the number of atoms that have decayed after 10 days.

[8]:

import numpy as np
from astropy import units as u
from astropy import constants as const

#initial number of atoms
n_0 = 1.0767e22
#half life
t_half = 6.10
#time in days
time = 10

#number of atoms keft after 10 days
n_final = n_0 * np.exp(-t_half * time)

#number of atoms that have decayed
n_decays = n_0 - n_final

The gammarays that are released during this radiocative decay can be released from a number of energy level transitions. Each transition has an associated energy and a probability out of 100 decays. From the combination of all of these tranisitions and their probabilities, the total energy released per decay is \(1.75 MeV\) [].

[ ]:

#energy per decay in eV
energy_per_decay = 1.75e6

total_energy = n_decays * energy_per_decay

print("The total energy released from radioactive decay of 1g of 56Ni after 10 days is:", total_energy, "eV")

The total energy released from radioactive decay of 1g of 56Ni after 10 days is: 1.884225e+28 eV