The half life of a radioactive substance is 20 minutes. The time taken between 50 % decay and 87.5 % decay of the substance will be

Question

The half life of a radioactive substance is 20 minutes. The time taken between 50 % decay and 87.5 % decay of the substance will be (A) 30 minutes (B) 40 minutes (C) 25 minutes (D) 10 minutes

Tardigrade Admin · Accepted Answer

Given, T1 / 2=20 min N1=50 N2=100-87.5=12.5 We know that, time taken by a substance to decay, t2-t1 =(T/ ln 2) ln ((N1/N2))=(20/ ln 2) ln [(50/12.5)] =(20/ ln 2) ln 4=40 min

Q. The half life of a radioactive substance is $20 min u t es$ . The time taken between $50%$ decay and $87.5%$ decay of the substance will be

30 minutes

40 minutes

25 minutes

10 minutes

Given, $T_{1/2} = 20 min$
$N_{1} = 50$
$N_{2} = 100 - 87.5 = 12.5$
We know that, time taken by a substance to decay,
$t_{2} - t_{1} = \frac{T}{l n 2} ln (\frac{N _{1}}{N _{2}}) = \frac{20}{l n 2} ln [\frac{50}{12.5}]$
$= \frac{20}{l n 2} ln 4 = 40 min$

Q. The half life of a radioactive substance is 20minutes. The time taken between 50% decay and 87.5% decay of the substance will be