11
Maths Internal Assessment
Mathematical Modelling of Radioactive Decay occurring due to Chernobyl
Disaster
2025 LATEST UPDATED VERSION
Introduction
We live in a world that is made up of many diverse items, materials, and scientific
phenomena. All of these things are based on a certain mechanism that is governed by a set of
rules, regulations, and assumptions. The building up of information about these assumptions
and principles aids in the formulation of a theory. The most fascinating element of science is
that it invites people like me to embark on a journey with the sole objective of discovering and
explaining the origins of scientific curiosity. Mathematical modelling is a key idea in
mathematics that allows us to assess a mathematical link between many phenomena that come
under different sectors or disciplines such as physics, chemistry, and biology. Mathematical
modelling also aids in the development of an expression for predicting or forecasting
phenomena based on real-world data. As a result, it is a crucial idea since it employs theoretical
assumptions to provide practical implications in the real world.
The major goal of this research is to employ mathematical modelling to explain or
forecast the phenomena of radioactive decay, which is related to the field of Nuclear Physics.
The model will provide a quantitative estimate of how long it takes for a radioactive element
to decay fully. The study's most intriguing feature is its focus on a man-made calamity that
may also be deemed a scientific tragedy. Here, I am referring to the Chernobyl accident, in
which the entire city was exposed to radiation. The goal of the research is to mathematically
investigate the process of radioactive decay using the exponential decay mathematical
technique. To begin, I'll provide theoretical background on the concepts of radioactive decay
and exponential decay, as well as the historical and scientific facts surrounding the Chernobyl
accident.
,11
The mathematical expression for describing the Caesium-137 decay, which was the largest
radioactive element exposed in the atmosphere, will be formulated using the theoretical
assumptions.
Chernobyl Disaster
It's critical to address the question of "what happened?" first. "What was the impact of
this event?" and "What was the impact of this event?" During World War II, when the United
States deployed nuclear weapons on Hiroshima and Nagasaki. The entire metropolis, including
the habitat living within it, was destroyed in the aftermath of this deed, which was witnessed
by the entire world. This catastrophe has made people realise the serious consequences of
employing nuclear weapons in warfare. Although countries are not now engaged in full-fledged
armed conflicts, they are nonetheless instrumental in the design of nuclear warheads to assure
their safety and integrity. Another argument for constructing nuclear power plants is that it has
proven to be a reliable source of electricity. Nuclear power facilities are not particularly safe
environments, as any mishap could result in the release or emission of large amounts of
radiation. On April 26, 1986, the Chernobyl nuclear power plant in Ukraine erupted, producing
or emitting massive amounts of radiation. It was actually in the form of microscopic radioactive
particles that were dispersed throughout the entire area where the incident occurred. The
radioactive particles travelled not just across Ukraine, but also throughout the European and
Western regions of the USSR (previously known as the Soviet Union).
This was deemed the worst nuclear power plant explosion scenario ever recorded in
history. The government was required to carry out a precise containment strategy that included
the hiring of over 500,000 workers and a budget of almost $18 billion. The catastrophe claimed
the lives of 31 people. People living in the surrounding areas, however, suffered from cancer
or other forms of deformity as a result of their exposure to radioactive particles in the long
term. In 2014, the radiation level in Chernobyl and Pripyat was assessed to be 192.72 million
Sieverts (a measurement unit for radiation output) according to the reports. Even yet, the
radiation level was high enough to be hazardous to the natural environment. Because a dose of
100 million Sieverts is considered the minimum required for everybody suffering from cancer.
The particles emitted following the explosion are now radioactive isotopes that are unstable.
Radioactive elements such as strontium-90, caesium-137, and iodine-131 may be present.
These elements' particles continue to emit radiation for a long time after they have entirely
decayed. Caesium-137, for example, takes about 30 years to achieve its half-life. This
, 11
incident occurred in 1986, thus it will take another 25 years for it to completely decay and
stop producing radiation.
Aim and Approach
The discussion above confirms the study's goal, which is to utilise mathematical
approaches to evaluate the Chernobyl radiation scenario. While seeing a video about the
Chernobyl tragedy, I was inspired to pursue this research. The hypothetical considerations will
then be utilized to create an expression to represent the radioactive decay of Caesium-137,
which was the most abundant radioactive element in the atmosphere at the time. Although, as
part of my Physics education, I studied the exponential method for estimating the number of
nucleus atoms that decay over time. The equation will be generated in this study utilising three
different mathematical modelling techniques: exponential decay model, cubic model, and
linear model. Each model's plot will be created and compared to the curve representing the real
observation to see which model has the least variance and is better at forecasting values based
on actual observations. The research would be significant in determining whether or not other
models can be utilised to forecast radioactive decay.
Data Collection and Results
I took an unusual technique to gathering data regarding the time required for Caesium-
137 decay. I utilised Microsoft Excel's "random number generator" tool. To accomplish this, I
first set the decay probability to 0.1. Because there were 137 nuclei in all, I used the value '1'
to represent the atom or nuclei that had not yet destroyed. As a result, the number of nucleus
atoms for Caesium-137 would be 137 at t=0. For t=1, I used the random formula to choose a
value of '0' to represent a decaying nucleus and a value of '1' to indicate an atom or nuclei that
has not yet decayed. This formula was stretched once more for a total of 137 cells. At t=1, the
number of nuclei remaining was calculated by adding all the random integers that were equal
to 1. For t = 2 through t = 100, the values of the remaining nuclei were determined in the same
way. These numbers represented the number of nuclei that remained. I estimated the difference
between the values of N at t=1 and t =0 in order to determine the decay nuclei. The difference
of N for t = n and t = n-1 was also calculated to corroborate the number of nuclei decaying at
each time interval. Based on this, 101 observations for the number of nuclei that had decayed
from t=0 to t=100 were acquired. Although, because the half-life of Caesium is 30 (as explained
above), the total breakdown of atoms occurs after t=60. As a result, I set the probability value
to 0.1, which ensures that the value reaches zero after t = 60. The 60 measurements for time
Maths Internal Assessment
Mathematical Modelling of Radioactive Decay occurring due to Chernobyl
Disaster
2025 LATEST UPDATED VERSION
Introduction
We live in a world that is made up of many diverse items, materials, and scientific
phenomena. All of these things are based on a certain mechanism that is governed by a set of
rules, regulations, and assumptions. The building up of information about these assumptions
and principles aids in the formulation of a theory. The most fascinating element of science is
that it invites people like me to embark on a journey with the sole objective of discovering and
explaining the origins of scientific curiosity. Mathematical modelling is a key idea in
mathematics that allows us to assess a mathematical link between many phenomena that come
under different sectors or disciplines such as physics, chemistry, and biology. Mathematical
modelling also aids in the development of an expression for predicting or forecasting
phenomena based on real-world data. As a result, it is a crucial idea since it employs theoretical
assumptions to provide practical implications in the real world.
The major goal of this research is to employ mathematical modelling to explain or
forecast the phenomena of radioactive decay, which is related to the field of Nuclear Physics.
The model will provide a quantitative estimate of how long it takes for a radioactive element
to decay fully. The study's most intriguing feature is its focus on a man-made calamity that
may also be deemed a scientific tragedy. Here, I am referring to the Chernobyl accident, in
which the entire city was exposed to radiation. The goal of the research is to mathematically
investigate the process of radioactive decay using the exponential decay mathematical
technique. To begin, I'll provide theoretical background on the concepts of radioactive decay
and exponential decay, as well as the historical and scientific facts surrounding the Chernobyl
accident.
,11
The mathematical expression for describing the Caesium-137 decay, which was the largest
radioactive element exposed in the atmosphere, will be formulated using the theoretical
assumptions.
Chernobyl Disaster
It's critical to address the question of "what happened?" first. "What was the impact of
this event?" and "What was the impact of this event?" During World War II, when the United
States deployed nuclear weapons on Hiroshima and Nagasaki. The entire metropolis, including
the habitat living within it, was destroyed in the aftermath of this deed, which was witnessed
by the entire world. This catastrophe has made people realise the serious consequences of
employing nuclear weapons in warfare. Although countries are not now engaged in full-fledged
armed conflicts, they are nonetheless instrumental in the design of nuclear warheads to assure
their safety and integrity. Another argument for constructing nuclear power plants is that it has
proven to be a reliable source of electricity. Nuclear power facilities are not particularly safe
environments, as any mishap could result in the release or emission of large amounts of
radiation. On April 26, 1986, the Chernobyl nuclear power plant in Ukraine erupted, producing
or emitting massive amounts of radiation. It was actually in the form of microscopic radioactive
particles that were dispersed throughout the entire area where the incident occurred. The
radioactive particles travelled not just across Ukraine, but also throughout the European and
Western regions of the USSR (previously known as the Soviet Union).
This was deemed the worst nuclear power plant explosion scenario ever recorded in
history. The government was required to carry out a precise containment strategy that included
the hiring of over 500,000 workers and a budget of almost $18 billion. The catastrophe claimed
the lives of 31 people. People living in the surrounding areas, however, suffered from cancer
or other forms of deformity as a result of their exposure to radioactive particles in the long
term. In 2014, the radiation level in Chernobyl and Pripyat was assessed to be 192.72 million
Sieverts (a measurement unit for radiation output) according to the reports. Even yet, the
radiation level was high enough to be hazardous to the natural environment. Because a dose of
100 million Sieverts is considered the minimum required for everybody suffering from cancer.
The particles emitted following the explosion are now radioactive isotopes that are unstable.
Radioactive elements such as strontium-90, caesium-137, and iodine-131 may be present.
These elements' particles continue to emit radiation for a long time after they have entirely
decayed. Caesium-137, for example, takes about 30 years to achieve its half-life. This
, 11
incident occurred in 1986, thus it will take another 25 years for it to completely decay and
stop producing radiation.
Aim and Approach
The discussion above confirms the study's goal, which is to utilise mathematical
approaches to evaluate the Chernobyl radiation scenario. While seeing a video about the
Chernobyl tragedy, I was inspired to pursue this research. The hypothetical considerations will
then be utilized to create an expression to represent the radioactive decay of Caesium-137,
which was the most abundant radioactive element in the atmosphere at the time. Although, as
part of my Physics education, I studied the exponential method for estimating the number of
nucleus atoms that decay over time. The equation will be generated in this study utilising three
different mathematical modelling techniques: exponential decay model, cubic model, and
linear model. Each model's plot will be created and compared to the curve representing the real
observation to see which model has the least variance and is better at forecasting values based
on actual observations. The research would be significant in determining whether or not other
models can be utilised to forecast radioactive decay.
Data Collection and Results
I took an unusual technique to gathering data regarding the time required for Caesium-
137 decay. I utilised Microsoft Excel's "random number generator" tool. To accomplish this, I
first set the decay probability to 0.1. Because there were 137 nuclei in all, I used the value '1'
to represent the atom or nuclei that had not yet destroyed. As a result, the number of nucleus
atoms for Caesium-137 would be 137 at t=0. For t=1, I used the random formula to choose a
value of '0' to represent a decaying nucleus and a value of '1' to indicate an atom or nuclei that
has not yet decayed. This formula was stretched once more for a total of 137 cells. At t=1, the
number of nuclei remaining was calculated by adding all the random integers that were equal
to 1. For t = 2 through t = 100, the values of the remaining nuclei were determined in the same
way. These numbers represented the number of nuclei that remained. I estimated the difference
between the values of N at t=1 and t =0 in order to determine the decay nuclei. The difference
of N for t = n and t = n-1 was also calculated to corroborate the number of nuclei decaying at
each time interval. Based on this, 101 observations for the number of nuclei that had decayed
from t=0 to t=100 were acquired. Although, because the half-life of Caesium is 30 (as explained
above), the total breakdown of atoms occurs after t=60. As a result, I set the probability value
to 0.1, which ensures that the value reaches zero after t = 60. The 60 measurements for time
