How Long Should Radiation Therapy Last After Two Years to Match Initial Dosage?

[somecelxis]

Homework Statement

a patient who is undergoing cancer theraphy is given 10 mins of irradiation from a radioactive source that has half life = 2 years. If the same source is to be used for same treatment 2 years later , how long should the patient should be irradiated?

the ans is 20 mins .. can someoene teach me how to do this?

Homework Equations

The Attempt at a Solution

i was told that:
at time = 0 (ie. Now) the patient undergoes 10 mins of irradiation. Let's say the amount of radioactivity of the source now is at 100%

We are told that it's half life is 2 years which means in 2 years the radioactivity of the source is at 50%.

So suppose it is 2 years later
if the patient's therapy lasts 10 min - he gets 50% dosage.
if the patients therapy goes another 10 min - he gets another 50% dosage
So a total of 20 min of therapy results in (50% + 50% = 100% same dosage as he received 2 years earlier)

but why if the patient's therapy lasts 10 min - he gets 50% dosage. ??[/B]

 

[BvU]

You're doing the right thing. Dosage is proportional to the time and to the radioactivity of the source: dosage is something like the amount of radioactive decays, so activity (decays/time) times time.

 

[NascentOxygen]

why if the patient's therapy lasts 10 min - he gets 50% dosage. ??

Instead of the patient, imagine there is a Geiger counter, and explain what it would record.