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halflife456 · Dec 20, 2010, 03:38 AM

1. Cobalt-60 is often used as a radioactive source in medical physics. It has a half-life of 5.25 years. Calculate how long after a new sample is delivered the activity will have to decreased to one-eighth of its value when delivered.

2. The half-life of a radioactive isotope of sodium used in medicine is 15 hours.
(a) Determine the decay constant for this nuclide.
(b) A small volume of a solution containing this nuclide has an activity of 12000 disintegrations per minute when it is injected into the bloodstreams of a patients. After 30 hours, the activity of 1.0 cm^3 of blood taken from the patient is 0.50 disintegrations per minute. Estimate the volume of blood in the patient, Assume that the solution is uniformly diluted in the blood, that it is not taken up by the body tissues, and that there is no less by excretion.

Curlyben · Dec 20, 2010, 03:41 AM

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galactus · Dec 20, 2010, 05:35 AM

Originally Posted by halflife456

1. Cobalt-60 is often used as a radioactive source in medical physics. It has a half-life of 5.25 years. Calculate how long after a new sample is delivered the activity will have to decreased to one-eighth of its value when delivered.

Half life is given by $T=\frac{-ln(2)}{k}\Rightarrow k=\frac{-ln(2)}{T}$

In this case, T is given as 5.25. Thus, the decay constant, k, can be found

$k=\frac{-ln(2)}{5.25}$

Now, you can use

$\frac{A}{8}=Ae^{kt}$

The A's cancel and we are left with:

$\frac{1}{8}=e^{kt}$

Sub in k and solve for t.

2. The half-life of a radioactive isotope of sodium used in medicine is 15 hours.

(a) Determine the decay constant for this nuclide.

Use the same method I outlined above.

(b) A small volume of a solution containing this nuclide has an activity of 12000 disintegrations per minute when it is injected into the bloodstreams of a patients. After 30 hours, the activity of 1.0 cm^3 of blood taken from the patient is 0.50 disintegrations per minute. Estimate the volume of blood in the patient, Assume that the solution is uniformly diluted in the blood, that it is not taken up by the body tissues, and that there is no less by excretion.

They are just asking for an estimate. Think about it. If the half life is 15 years, then how much remains after 30 hours? Half life means 1/2 remains after 15 years, then half of that in another 15. So, 3/4 has decayed in 30 hours.
If the subject was injected with 12,000, then what remains in 30 hours?
Compare this to the amount in 1 cc. Remember, 1 cc is 1 ml.