Acertain 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

3.07 seconds is the half-life of the isotope.

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 =

Formula used :

where,

= initial mass of isotope

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

= half life of the isotope

= rate constant

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

3.07 seconds is the half-life of the isotope.

answer : third trial had the contaminated sample and the correct value for dhrxn should be 1000 kj/mol

explanation :

let us write down the given equations

equation 1 :

equation 2 :

equation 3 :

let us use hess's law to find out which 2 equations can be added to get the third equation.

let us reverse equation 2 and multiply it by 2. the new equation that we get is,

equation 4 :

let us add equation 1 & 4

the above equation is similar to equation 3 but has different value for dhrxn.

therefore third trial had the contaminated sample and the correct value for dhrxn should be 1000 kj/mol