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Old Oct 21st 2014, 10:05 AM   #1
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Half life of substance

cancer 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?
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Old Oct 21st 2014, 01:16 PM   #2
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half life is 10 years, so after ten years the sample has only half as many radioactive ions as originally. Hence its rate of alpha particle emission is 1/2 as much, so it takes twice as long to emit the same number of particles.
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Old Oct 22nd 2014, 06:19 AM   #3
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Originally Posted by ChipB View Post
half life is 10 years, so after ten years the sample has only half as many radioactive ions as originally. Hence its rate of alpha particle emission is 1/2 as much, so it takes twice as long to emit the same number of particles.
can you explain further?
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Old Oct 22nd 2014, 08:16 AM   #4
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I assume that the cancer patient needs to receive a certain amount of radiation for each treatment - call it P particles. The time required for each treatment is then equal to the number of particles required to be emitted divided by the rate of particle emission:

T_treatment= P/R

The rate of particle emission slows down as the radioactive source ages:

R(t) = R_0 x (1/2)^(t/t_hl)

where R_0 is the initial rate of particle emission, and t_hl is the half life of the material. In this case you have t=2 years, t_hl = 2 years, so:

R(2 years) = R_0 x (1/2)^1 = R_0/2.

The time initially required for treatment at t=0 years is

T_treatment = P/R_0 = 10 minutes.

The time required for treatment at t=2 years is:

T_treatment = P/(R_0/2) = 2 P/R_0 = 2 x 10 minutes = 20 minutes.
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