Question

A certain radioactive isotope takes 8.40 s for 85.0% of the isotope to decay. What is the half-life of the isotope?

1.0 s


3.07 s


4.02 s


1.25 s


12.5 s

Answer 1

3.07 seconds is the half-life of the isotope.

Step-by-step explanation:

Initial mass of an isotope = x

Time taken by the sample, t = 8.40 s

Mass of an isotope decayed= 85.0%

Final mass of an isotope left=(100%-85%)of x= 15.0% of x = 0.15x

Half life of an isotope =
`t_{(1)/(2)} = ?`

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

`\lambda` = rate constant

`0.15x=x* e^{-((0.693)/(t_(1/2)))* 8.40 s}\\\\N=N_o* e^(-0.693)`

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

`t_{1/2]=3.07 s`

3.07 seconds is the half-life of the isotope.