A radioactive isotope source has a mass of 120ug. If the isotope had a half life of 20s, what would be the mass if the isotope after 2 mins?
k = 0.693/t1/2
Then
ln(No/N) = kt
No = 120 ug
N = solve for this
k = from above
t = 120 sec.
To calculate the mass of the isotope after 2 minutes, we need to determine the number of half-lives that have elapsed during that time period.
First, let's convert the time into seconds:
2 minutes = 2 * 60 = 120 seconds
Next, we need to calculate the number of half-lives that have passed. We can do this by dividing the total time elapsed by the half-life:
Number of half-lives = Total time elapsed / Half-life
Number of half-lives = 120 seconds / 20 seconds = 6 half-lives
Now, we need to calculate the remaining mass after 6 half-lives. Each half-life reduces the mass to half of its previous value.
Mass after 6 half-lives = Initial mass * (1/2)^(number of half-lives)
Mass after 6 half-lives = 120 ug * (1/2)^6
Simplifying the equation:
Mass after 6 half-lives = 120 ug * (1/64)
Mass after 6 half-lives = 1.875 ug
Therefore, the mass of the isotope after 2 minutes would be 1.875 ug.