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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