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?
Someone please help me with this question.
To find the activity of 1 gram of Ra-226, we need to use the decay constant (λ) and the Avogadro's number (NA).
The decay constant (λ) can be found using the half-life (T1/2) of Ra-226 using the formula:
λ = ln(2) / T1/2
Plugging in the given half-life of Ra-226 (T1/2 = 1602 years), we can calculate the decay constant (λ):
λ = ln(2) / 1602
Next, we need to find the number of radioactive atoms present in 1 gram of Ra-226. We can calculate this using Avogadro's number (NA = 6.022 x 10^23 atoms/mol) and the molar mass (molar mass of Ra-226 = 226 g/mol):
Number of atoms = (1 gram / 226 g/mol) * NA
Now, we know the decay constant (λ) and the number of radioactive atoms. We can calculate the activity (A) using the formula:
Activity (A) = λ * Number of atoms
To convert the activity to curies (Ci), we use the conversion factor 3.7 x 10^10 Bq = 1 Ci.
Let's calculate the activity of 1 gram of Ra-226:
1. Calculate the decay constant (λ):
λ = ln(2) / 1602
2. Calculate the number of atoms:
Number of atoms = (1 gram / 226 g/mol) * NA
3. Calculate the activity:
Activity (A) = λ * Number of atoms
4. Convert the activity to Ci:
Activity (Ci) = Activity (A) / (3.7 x 10^10 Bq/Ci)
To find the activity after 1T1/2 and 5T1/2, multiply the initial activity by the decay constant raised to the respective power:
Activity_after_1T1/2 = Activity * (λ)^1
Activity_after_5T1/2 = Activity * (λ)^5
Let's perform the calculations to find the activity and the activity after 1T1/2 and 5T1/2 for 1 gram of Ra-226.