Question

How long does it take a 100 g sample of As-81 to decay to 6.25 g? (half-life of As-81 is 33 seconds)

Answer 1

Step-by-step explanation:

m₀ = 100 g

m = 6.25 g

T = 33 s

_____________

t - ?

Radioactive decay constant:

λ = ln 2 / T = 0.693 / 33 ≈ 0.021 s⁻¹

Law of radioactive decay:

`m=m_(0) e^(-\lambda t) \\`

`e^(-\lambda t) = (m)/(m_0) \\`

`ln (e^(-\lambda t)) = ln((m)/(m_0) ) \\`

`-\lambda t = ln ((m)/(m_0))`

`t = -(ln((m)/(m_0)) )/(\lambda)`

t = - ln (6.25/100) / 0.021 ≈ 132 s