Resource Lesson
Radioactive Halflife
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The formula used to calculate the
number of remaining undecayed atoms
N
after a period of time
t
:
N = ( ½
n
) N
o
where
n
is the ratio of the time passed to the length of one half-life = t / T
½
, and
N
o
represents the original number of nuclei present in the sample.
In the above formula, you must know the half-life which may be measured in any length of time as long as
t
is also measured in the same units. Using the graph shown above, the half-life is approaximately 2.6 seconds since at that moment there are 100 undecayed nuclei still remaining of the original 200.
The formula that relates the
decay constant λ and half-life T
½
is
λ T½ = 0 .693
where
λ and T
½
must be in corresponding units of measurement
The formula used to calculate the number of remaining undecayed atoms if you are given
the decay constant, λ
and
amount of time
is
N = N
o
e
- λt
where
λ
is the decay constant which can have units of "per second," "per hour," or "per year"
as long as time
t
has the same time measurment.
The formula used to calculate the activity of a radioactive sample is
A = - λN
where
A
, which in the SI system is measured in Becquerels (decays per second)
The following five questions are related to the same situation.
One of the radioactive waste products of a reactor has a half-life of 250 years. What fraction of a given sample of this product will remain after 750 years?
A 1/9
B 1/8
C 1/6
D 1/3
What is the decay constant for this radioactive product?
A 2079 yr
-1
B 5.544 yr
-1
C 0.002772 yr
-1
D 0.000927 yr
-1
If there were only 1000 nuclei in the original sample, what would be the activity rate of the remaining sample after 750 years?
A 0.3465 nuclei per year
B 0.3080 nuclei per year
C 0.1155 nuclei per year
D 0.1027 nuclei per year
A 48 gram sample of a radioactive nuclide decayed to 3 grams of the nuclide in 36 minutes. How many grams of the original nuclide sample remained after the first 27 minutes?
A 12 grams
B 8 grams
C 6 grams
D 1 gram
What is the activity rate in grams/minute of the radioactive sample at 36 minutes?
A 21.33 grams/minute
B 3.693 grams/minute
C 1.333 grams/minute
C 0.231 grams/minute
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