Question

The half life of a radioactive element is 40 minutes the amount that will decay in 2 hours?

Answer 1

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Answer 2

Given :

Half life of a radioactive element is 40 minutes.

To find :

Amount decayed in 2 hours

Solution :

We know that , Number of active nuclei left after time 't' is given by

N = N•e^-kt

Also , Half life of Radioactive material is given by

T(Half life) = ln2/k

k.T = ln2

where k is decay constant

=> k(40) = ln2 ______(1)

So, at t = 2hours i.e. t = 120 minutes

Number of active nuclei left will be

N = N•e^-k(120)

N = N•e^-k(40).3

From (1)

N = N•e^-3.ln2

N = N•e^-ln8

N = N•/8

Number of active nuclei after two hours are N•/8 i.e.

(N•/8)/N• ×100 = 12.5 %

So amount of matter that decays after two hours if half life of substance is 40 minutes is 100-12.5

i.e. 87.5 %