Answer: 0.0102 micrograms
Explanation:
Given t1/2 for 231Pa = 3.25 x 10^4 yr
The radioactive disintegration constant is related by the equation as,
λ = 0.693/t1/2
λ = 0.693/(3.25 x 10^4) yr-1
λ = 2.1323 x 10^-5 yr^-1
Now radioactive disintegration follows first order rate law so we get a equation,
N(t) = N0e^-λt
Where N0 = Amount initially present = 10.40 microgram
Nt = amount present after time t = need to be calculate
λ = radioactive disintegration constant = 2.1323 x 10^-5 yr^-1
t= time = 3.25 x 10^5 yr
Now from the above equation we get,
N(t) = N0e^-λt
Nt = 10.40e^(2.1323^10-5 x 3.25^105)
Nt = 10.40 x e^-6.9299
Nt = 10.40 x 9.78 x 10^-4
Nt = 0.0102 micrograms
