Suppose a patient is given 140mg of I−131, a beta emitter with a half-life of 8.0 days.
Assuming that none of the I−131 is eliminated from the person's body in the first 4.0 hours of treatment, what is the exposure (in Ci) during those first four hours?
Express your answer using two significant figures.
that is wrong Ci does not equal 1
To find the exposure (in Ci) during the first four hours, we need to determine the initial amount of I−131 and calculate the decay during that time period.
Given:
Initial amount of I−131 = 140 mg
Half-life of I−131 = 8.0 days
To calculate the initial amount of I−131 (N₀) in Ci, we need to convert the mass (in mg) to activity (in Ci) using the specific activity of I−131. The specific activity represents the radioactivity per unit mass.
Assuming the specific activity of I−131 is 1 Ci/g (this value might vary), we can convert the mass to Ci:
N₀ = (140 mg) * (1 Ci/1 g) = 140 Ci
Now, let's calculate the decay during the first four hours.
Since the half-life of I−131 is 8.0 days, we first need to convert four hours into days. There are 24 hours in a day.
Time (t) = (4 hours) / (24 hours/day) = 0.1667 days
We can use the radioactive decay equation to calculate the remaining amount of I−131 (N) after time t:
N = N₀ * (1/2)^(t / T)
Where:
N₀ = Initial amount of I−131
N = Remaining amount of I−131 after time t
t = Time in days
T = Half-life of I−131
Plugging in the values:
N = 140 Ci * (1/2)^(0.1667 / 8.0)
Calculating the expression:
N ≈ 134 Ci
Therefore, the exposure (in Ci) during the first four hours is approximately 134 Ci.
k = 0.693/t1/2
k = approx 0.09 but you should get a more accurate number.
Convert 140 mg to number of atoms initially (at time = 0)
Use ln(No/N) = kt to determine N = number of atoms after four hours.
The difference between initial and after 4 hours is atoms that decayed in 4 hours.
Then 3.7E10 decays per second = 1 Ci