Radioactive decay Flashcards
The carbon content of living trees includes a small proportion of C-14, which is a radioactive isotope. After a tree dies, the proportion of C-14 in it decreases due to radioactive decay.
Suggest why the method of carbon dating is likely to be unreliable if a sample is:
a) < 200 years old
b) > 60,000 years old
a) it is difficult to measure the small change in activity accurately.
b) There would be very little to decay
State the name of the exchange particle involved in beta+ decay
W+ boson
State and explain why environmentalists might have been concerned by the use of such a large quantity of Pu-238
- toxic
- harmful if released into atmosphere
- alphas dangerous when ingested
State and explain whether the activity of a given number of atoms of plutonium is affected when they are in form of plutonium oxide
unaffected
chemical bonding involves electrons
radioactivity is nuclear
The activity of a radioactive sample =
number of nuclei decaying per second (Bq)
unit for activity
Becquerel where 1Bq = 1 decay/second
Activity, A =
delta N / delta t = decay constant * number of nuclei = N * -lambda (negative as the number of atoms is decreasing)
Activity is proportional to
the number of nuclei therefore amount of activity is proportional to the amount of material present
Unit for N
nuclei
Decay constant, lambda =
the probability of a nucleus decaying per second
= delta N / delta t * N
= rate of change of N / N
A high value of lambda means
a high rate of decay
usually very small (10^-5 sometimes) but can be > 1
The number of unstable nuclei remaining, N =
N0 * e^(-lambda * t)
The activity of a radioactive sample, A =
A0 * e^(-lambda * t)
For a source emitting particles of photons of the same energy, E, the energy transfer per second = the power of the source =
A*E
Define half life
the average time taken for the number of nuclei present in an isotope to halve
Half life = T1/2 =
ln2 / lambda = 0.69 / lambda
To find the half-life from a graph…
use the time it takes for the activity to fall to half the original value i.e. t=0
Number of half lives. n =
t / 2*T1/2
Remaining number of nuclei after n half lives, N =
N0 * 2^-n
The corrected count rate, C is directly proportional to… and so is equal to…
the activity of the source, A
so C= C0 * e^(-lambda * t)
where C0 is the count rate at t=0
Mass, M is directly proportional to… so is equal to
the number of nuclei, N
so m = m0 * e^(-lambda*t)
where m0 is the mass at t=0
Graph of mass (y axis) against time (x axis)
cuts y axis at m0
tends towards t=0 exponentially
Carbon dating:
living plants and trees absorb C-14 and when they die they stop taking it in and so the proportion of C-14 decreases as the nuclei decay. Activity is proportional to the number of atoms still to decay so measuring the activity of the dead sample enables its age to be calculated. Activity falls with half life which can be tested to date them.
Argon dating:
rocks contain trapped argon as a result of the decay of radioactive isotope of potassium into argon via electron capture. The age of the rock can be calculated by measuring the proportion of argon gas to potassium
Mole =
amount of a substance containing same number of particles (NA = Avagadro’s constant = 6.022x10^23) as there are in 12g of carbon-12
1 mole of C-12 has _____ molecules and weights
NA = 6.022x10^23
12g
Moles to mass (g) conversion
1 mole = atomic mass (g)
Mass (g) to atoms conversion
atomic mass (g) = 6.022x10^23 (NA) particles
Moles to atoms conversion
1 mole = 6.022x10^23 (NA) particles
When a nucleus emits an alpha or a beta particle it becomes a nucleus of a different _____ because the ______. The number of nuclei of the initial isotope therefore _____ as does the _____ (but just gradually).
element
proton number changes
decreases
mass
