Question

Manganese-56 is a beta emitter with a half-life of 2.6 h. what is the mass of manganese-56 in a 1.0-mg sample of the isotope at the end of 10.4 h?

Answer 1

Answer: 0.0625

Step-by-step explanation:

Answer 2

The mass at time may be expressed by

`m(t) = m_(0) e^(-kt)`
where
m₀ = the original mass
k = decay constant
t = time, hours

Because the half-life is 2.6 h, therefore

`e^(-2.6k) = 1/2 \\ -2.6k = ln(1/2) \\ k = (ln(1/2))/(-2.6) =0.2666`

Since m₀ = 1.0 mg, the mass after 10.4 hours is

`(1.0 \, mg)e^(-0.2666*10.4) = 0.0625 \, mg`

Answer: 0.0625 mg