Question

The half-life of a radioactive nuclide is 2.5hrs. What fraction of a sample of this nuclide would remain after 12.5 hrs

Answer 1

0.03127 fraction of a sample of this nuclide would remain after 12.5 hrs.

Step-by-step explanation:

Initial mass of the isotope =
`N_o`

Time taken by the sample, t = 12.5 hour

Formula used :

`N=N_o* e^(-\lambda t)\\\\\lambda =\frac{0.693}{t_{(1)/(2)}}`

where,

`N_o` = initial mass of isotope

N = mass of the parent isotope left after the time, (t)

`t_{(1)/(2)}` = half life of the isotope = 2.5 hour

`\lambda` = rate constant

`N=N_o* e^{-((0.693)/(2.5 hours))* 12.5 hour}`

Now put all the given values in this formula, we get

`N=N_o* e^(-3.465)`

`(N)/(N_o)=0.03127`

0.03127 fraction of a sample of this nuclide would remain after 12.5 hrs.