Answer :
To find the half-life of astatine-218, we can use the formula:
t1/2 = (ln(2) / λ)
Where t1/2 is the half-life, ln is the natural logarithm, and λ is the decay constant.
Given that the mass of the sample decays from 64.5 micrograms to 7.48 micrograms in 6.22 seconds, we can calculate the decay constant using the formula:
N = N0 * e^(-λt)
Where N is the final mass, N0 is the initial mass, e is the base of the natural logarithm, λ is the decay constant, and t is the time.
Plugging in the values, we have:
7.48 = 64.5 * e^(-λ * 6.22)
Solving for λ, we find:
λ = -ln(7.48/64.5) / 6.22
Now that we have the decay constant, we can calculate the half-life using the formula:
t1/2 = (ln(2) / λ)
Plugging in the value of λ, we get:
t1/2 = ln(2) / (-ln(7.48/64.5) / 6.22)
Calculating this value, we find that the half-life of astatine-218 is approximately 8.62 seconds.
To know more about astatine visit:
https://brainly.com/question/33861464
#SPJ11
