Co-60 Unit Activity: Treatment Time Calculation

AI Thread Summary
The discussion focuses on calculating the treatment time for a second cancer patient using a cobalt-60 unit after a 1.5-year interval. The decay constant is established as 0.1 months^-1, leading to an activity level of 16.5% of the original after this period. Consequently, the treatment time for the second patient would need to be 83.5% longer than that of the first patient due to the decreased activity. The key point raised is the need for consistency in the quantity of radiation delivered during each treatment. This highlights the importance of understanding radioactive decay in treatment planning.
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Homework Statement


A patient is treated for cancer using radiation from a cobalt-60 unit. Exactly 1.5 years later another patient is treated for the same cancer using the same co-60unit previously used. How much longer would treatment be for the second patient?

Homework Equations


Decay Constant (λ)
A(t)= Activity after 1.5 years
A0= original activity

A(t)=A0(e^-λt)
=A0(0.165)
Therefore the activity after 1.5 years is 16% of the original activity, so the treatment time would be 83.5% longer than the original treatment time

The Attempt at a Solution


Decay Constant (λ)= 0.1 months^-1

A(t)=A0(0.165)
Therefore the activity after 1.5 years is 16.5% of the original activity, so the treatment time would be 83.5% longer than the original treatment time
 
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What quantity should be the same for each treatment?
 
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