Question

A `Bi^(210)` radionuclide decays via the chain
`Bi^(210)underset(lambda_1)rarr P_(0)underset(lambda_(2))rarrPb^(206)(stabl e)`
where the decay constants are `lambda_(1)=1.60.10^(-6)s^(-1), lambda_(2)= 5.80.10^(8)s^(-1)`. Calculate alpa-disintegrations and four `beta-` disintegrations ?

Answer 1

We have the chain
`underset(A_1)(B_i^210)underset(lambda_1)overset(beta)rarrunderset(A_2)(P_0^210)underset(lambda_2)overset(alpha)rarrunderset(A3)(P_b^206)`
of the previous problem initially
`N_(10)=(10^(-3))/(210)xx6.023xx10^(23)= 2.87xx10^(18)`
A month after preparation
`N_(1)= 4.54xx10^(16)`
`N_(2)= 2.52xx10^(18)`
using teh results of the previous problem
Then `A_(beta)= lambda_(1)N_(1)= 0.735xx10^(11) dis//sec`
`A_(alpha)= lambda_(2)N_(2)= 1.46xx10^(11) dis//sec`