Question

one of the radioactive materials released during the Fukishima disaster was cesium-134, cesium-134 has a half life of 2.1 years. How long will it take for this material to lose the following amount of it's radioactivity:

A: 90%

B: 99%

C: 99.9%

Answer 1

Solution:

cesium-134 has a half life of 2.1 years

Let initial amount is P_o

So P(t) =P_o e^kt

Half life = 2.1

so t = 2.1 P(t) = P_o/2

So Po/2 = P_o e^k*2.1

k= ln(1/2)/2.1 = -0.33

So, time taken to lose material during radioactive process

t = ln(P(t)/P_o)/k

for (A) 90% lose means P(t) = 10%Po = 0.1P_o

t = ln (0.1 P_{o/Po) /-0.33 = 6.98 Year}

(B)

for (B) 99% lose means P(t) = 1%Po = 0.01P_o

t = ln (0.01 P_{o/Po) /-0.33 = 13.95 Year}

(C)

99.9% lose means P(t) = 0.1%Po = 0.001P_o

t = ln (0.001 P_{o/Po) /-0.33 = 20.93 Year}