T1/2(Ra-226) = 1602 years
What is the activity of 1 gram of Ra-226? Give the answer in Ci and Bq?
What would be this activity after 1T1/2 and 5T1/2?
Would appreciate if someone could show me how to do this question. Thanks.
To find the activity of 1 gram of Ra-226, we need to use the radioactive decay formula:
A = A0 * e^(-λt)
Where:
A = Activity at time t
A0 = Initial activity
λ = Decay constant
t = Time
First, let's find the decay constant (λ), which is given by:
λ = 0.693 / T1/2
For Ra-226, T1/2 = 1602 years. Plugging this value in, we get:
λ = 0.693 / 1602
Calculating this, λ = 0.00043 years^-1.
Now, let's find the activity (A) of 1 gram of Ra-226. We'll assume that the initial activity (A0) is 1 Ci (Curie), which is equal to 3.7 x 10^10 Bq (Becquerels).
Using the formula A = A0 * e^(-λt) and plugging in the values, we have:
A = (1 Ci) * e^(-0.00043 * t)
To calculate the activity in Ci, we can use the relationship 1 Ci = 3.7 x 10^10 Bq.
To find the activity after 1T1/2 and 5T1/2, we substitute the respective values of t into the equation.
After 1T1/2:
t = 1 * T1/2 = 1 * 1602 years
After 5T1/2:
t = 5 * T1/2 = 5 * 1602 years
By plugging these values into the equation, we can calculate the activities in Ci and Bq.
Please note that these calculations assume constant decay rates and no other sources of Ra-226 contamination.