8.2 - Radioactive Decay Flashcards
What is the definition of radioactive decay?
The spontaneous disintegration of a nucleus to form a more stable nucleus, resulting in the emission of an alpha, beta or gamma particle.
Is the rate of decay affected by the surrounding conditions?
No, radioactive decay is a random process
What is the only thing you can estimate with radioactive decay?
The proportion of nuclei decaying in a given time period (the half life).
What does the count rate of a GM tube represent?
The number of decays.
What do the fluctuations in the count rate of a GM tube provide?
Evidence for the randomness of radioactive decay.
What is the decay constant? (λ)
The probability that an individual nucleus will decay per unit of time.
What is the suggested activity rate of a sample that is highly radioactive?
It has a high level of activity.
What is the equation for calculating the activity of a radioactive source?
A = - ΔN /Δt = λN
A = activity of the sample (Bq)
ΔN = number of decayed nuclei
Δt = time interval (s)
λ = decay constant (s⁻¹)
N = number of nuclei remaining in a sample
What is the activity of a sample measured in?
Becquerels (Bq)
1 Bq = one decay per second (1s⁻¹)
What are 3 things the equation calculating activity show?
- The greater the decay constant, the greater the activity (of the sample)
- The activity depends on the number of un-decayed nuclei remaining in the sample
- The minus sign indicates that the number of nuclei remaining decreases with time
What is the shape of a graph that shows the number of un-decayed nuclei against time?
Negative exponential decay. (starts high on the y axis).
From the graph of un-decayed nuclei against time, what shows a smaller decay constant?
If the exponential decay line is shallower.
What is the symbol for the initial number of un-decayed nuclei?
N₀
What is the equation for the number of un-decayed nuclei within a certain time?
N = N₀e^–λt
N = number of un-decayed nuclei at a certain time t
N₀ = the initial number of undecayed nuclei (When t=0)
λ = decay constant (s⁻¹)
t = time interval (s)
Using the equation for finding the number of un-decayed nuclei, what other quantities can you substitute in and why?
A = A₀e^–λt
activity - directly proportional to N (number of un-decayed nuclei)
C = C₀e^–λt
count rate - related to activity of the sample
What is the inverse function of e^x?
ln(y) (natural log)
e^x = y
x = ln(y)
What is Avogadro’s constant?
6.02 x 10²³mol⁻¹
(The number of atoms in one mole of a substance)
How do you get the number of nuclei using Avagadro’s constant? (equation)
Number of nuclei =
(mass x (6.02 x 10²³)) / molecular mass
What is half-life?
The time taken for the initial number of nuclei to halve for a particular isotope.
What is the equation for half-life?
𝑇½ = ln 2 / λ
𝑇½ = half life
ln 2 = natural log 2
λ = decay constant
How do you find the decay constant from a activity/time graph?
Find the half-life (where the activity halves) then put it into the equation
𝑇½ = ln 2 / λ
How do you calculate the number of atoms remaining after a certain time (on an activity/time graph)?
Find the activity at time t.
Use the equation A = λN to calculate N
What is the most common isotope used in carbon dating?
Carbon-14
What is carbon dating?
A highly reliable ageing method that predicts the age of organic materials/organisms.
What is the time period in which carbon dating is effective?
Around 1000 years to a limit of 40 000 years.
Why is carbon dating not possible if 1000 years haven’t passed?
The activity is too high so it is difficult to accurately measure the small change in activity.
Why is carbon dating not possible after 40000 years has passed?
The activity will be too small and have a count rate similar to background radiation.
How is radioactive waste stored?
In water tanks or sealed underground.
Why must radioactive waste be stored so effectively?
Because of the long half-lives of the isotopes used, the waste is radioactive for a long time after use (and is still harmful).
How would you interpret N = N₀e⁻λᵗ as a straight line graph equation?
y = mx + c
ln(N) = ln(N₀) -λt
ln(N) = y axis
ln(N₀) = y intercept
t = x-axis
-λ = gradient
How has potassium-argon dating occcured?
ancient rocks contain trapped argon gas as a result of the decay of the radioactive isotope of potassium-40.
This happens when a potassium nucleus captures an inner shell electron (electron capture).
What are the decay equations of potassium-argon dating?
electron capture:
⁴⁰K + e⁻ –> ⁴⁰Ar + Ve
potassium isotope can also decay by B⁻ emission
⁴⁰K –> ⁴⁰Ca + B⁻ + /Ve/ (/Ve/ = anti-neutrino)
What is potassium-argon dating used for?
Potassium-40’s half-life is 1.25 BILLION years.
The age of the rock (when its solidified) can be calculated by measuring the proportion of argon-40 to potassium-40.
It is used for dating rocks that are up to 100 million years old.
What is uranium-lead dating used for?
Dating geologic events more than 100 million years old.
How does uranium-lead dating work?
Uranium atoms decay whilst the number of lead atoms increases.
Uranium decays via a decay chain which ends with lead-206 (a stable isotope)
Why is uranium-lead dating the most accurate?
Uranium has been studied a lot more and its decay constant is better known than other isotopes, therefore it is more accurate.
