A clinical technician finds that the activity of a sodium-24 sample is 1,024 cpm. What will be the activity of the sample (in cpm) 90 h later if the half-life of sodium-24 is 15 h?
To determine the activity of the sodium-24 sample 90 hours later, we can use the formula for radioactive decay:
A(t) = A0 * (1/2)^(t/T)
Where:
- A(t) is the activity at time t
- A0 is the initial activity
- t is the elapsed time
- T is the half-life of the substance
Given:
- A0 = 1024 cpm
- t = 90 hours
- T = 15 hours
Plugging in these values:
A(90) = 1024 * (1/2)^(90/15)
A(90) = 1024 * (1/2)^6
A(90) = 1024 * (1/64)
A(90) = 16 cpm
Therefore, the activity of the sodium-24 sample 90 hours later will be 16 cpm.