Question

If 250 mg of a radioactive element decays to 190 mg in 24 hours, find the half-life of the element. (Round your answer to the nearest whole number.)

Answer 1

61 hours

Step-by-step explanation:

In this question we will use radioactive decay model

`m(t)=m_02^{-(t)/(h)}`

m0= 250 mg

h is the hlf life of element

m(t) is the mass left after t time

so,

`198=250*2^{-(24)/(h)}`

solving this equation for h

reaaranging and taking ln on both the sides we get

`ln2^{-(24)/(h)}= ln((190)/(250))`

solving further we get

h= 60.62 hours ≅61 hour

the half life of element is 61 hours