Question

In: Chemistry

the half-life of a radioisotope 63 hours how much time will elapse if the radioisotope decays...

the half-life of a radioisotope 63 hours how much time will elapse if the radioisotope decays to one-fourth of its original mass?

Solutions

Expert Solution

Ans:

Let the original mass be m1

Let the molar mass of the isotope be ‘M’.

No. of isotope initially, No = (m1/M) x NA                               {NA = Avagadro’s no = 6.023 x 1023}

Mass after the decay, m2 = m1/4

No. of isotopes after the decay, Nt = (m2/M) x NA = (m1/4M) x NA

Half-life, t½ = 63 hours

λ = decay constant = 0.693/t½ = 0.693/63 = 0.011 hours-1

We know that all radioactive decay follows first order kinetics. Accordingly, we have

Nt = No . e(-λt)

where, Nt = no of radioactive isotopes after the decay

            No = Initial no of radioactive isotopes

            λ = decay constant

t = time taken for decay =?

(m1/4M) x NA = {(m1/M) x NA} e(-0.011 x t)

t = 126 hours

OR

In a first order reaction for original mass to become half, it takes 1 half-life. For original mass to become 1/4th of its original mass it takes 2 half-life.

So, t = 2t½ = 2 x 63 = 126 hours


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