10.1 - models, radioactive decay Flashcards
What is a computational model?
A simplified artificial world with objects and rules that you create to model a scenario
What does an exponential relationship mean?
The rate of change of a quantity is proportional to the amount of the quantity there is
In radioactive decay, what is p?
The probability of a nucleus decaying
In radioactive decay, what is N?
The number of non-decayed nuclei left
What external conditions can the decay of a nucleus be affected by?
It cannot be affected by any external conditions.
The decay of a nucleus is a quantum event and it cannot be predicted or controlled
What is the equation for the probability of a nucleus decaying in a given time period?
p = λΔt
What is the symbol for the decay constant?
λ
What is the decay constant?
The probability of decay in a fixed time period
What is the symbol for activity?
a
lowercase
What is activity?
The number of decays happening per second
What are the units of activity?
Becquerel, Bq
s^-1
What is the equation for activity?
a = λN
What is the differential equation used in nuclear decay?
dN/dt = -λN
What is the symbol for half life?
t1/2
What is the half life?
The time taken for the activity or N to half its original starting value
What is the equation for finding the number of non-decayed nuclei at a given time?
N = N0e^-λt
What is the equation for finding the activity at a given time?
a = a0e^-λt
What is the equation for finding the half life?
t1/2 = ln2/λ
What is the equation for finding the decay constant?
λ = p/Δt
Using the half life, how can N be calculated for a given time?
N0 x 1/2^x
where x is the number of half lives passed
Using the half life, how can a be calculated for a given time?
a0 x 1/2^x
where x is the number of half lives passed
If a linear semi-log graph was plotted for nuclear decay, what equation would be used and what would the graph show?
lna = -λt - ln a0
The gradient is the decay constant, λ
The y-intercept is ln of a0
What is the equation for the number of non-decayed nuclei left when time passed is the half life?
lnN = lnN0 - ln2
How does radiocarbon dating work?
All living things have a constant ratio of carbon-12 to carbon-14 (a radioactive isotope of carbon). When they die, they stop taking in carbon, carbon-14 decays and so the amount of carbon-14 compared to carbon-12 decreases. This decreasing ratio is used to find the time since death.
Roughly what is the half life of carbon-14?
5730 years
What is the radioactive isotope of carbon?
carbon-14
What isotope of carbon is most common?
carbon-12
What will happen to the activity if the half life is shorter?
The activity will be greater
