How fast is the sample decaying after
5 min?
1. A 100-mg sample of thorium-233 (Th-233)
is placed into a nuclear reactor. After 10 min,
the sample has decayed to 73 mg. Use the
equation N(t)-Noe to answer the following
questions.
a) Determine the disintegration constant à for
Th-233.
b) Determine the half-life of Th-233.
d) Write the equation that gives the amount of
Th-233 remaining as a function of time, in
terms of its half-life.
2. The mass of radon, in milligrams, as a
function of time is given by the function.
Maalt)-Mo
, where Mo is the initial
mass of radon, and Ma. is the mass of radon
at time t, in days.
a) How much radon will remain after
i) 1 day?
ii) 1 week?
b) How long will it take for a sample of radon
to decay to 25% of its initial mass?
At what rate is the radon decaying at each
of these times?
Use the following information to answer
questions 2 to 4.
Radon-222 (Rn-222) is a radioactive element that
spontaneously decays into polonium-218 (Po-218)
with a half-life of 3.8 days. The atoms of these
two substances have approximately the same mass.
Suppose that the initial sample of radon has a mass
of 100 mg.
3. As radon decays, polonium is produced. The
mass of polonium, Mrs in milligrams, as
a function of time is given by the function
Mpo(t) = Mol 1 -
- Mo[1-(2), wh
, where Mo is the
initial mass of radon and t is time, in days.
a) How much polonium is there
initially?
after 1 day?
b) Find the first derivative of this
function. Explain what it means.
Fig: 1