Cesium137 a beta emitter has a halflife of 30 y How many yea

Cesium-137, a beta emitter, has a half-life of 30 y. How many years are required for 28 mg of cesium-137 to decay to 3.5 mg of cesium-137? 90 years 120 y 150 y 180 y 210 y 240 y

Solution

The time taken can be calculated with the formulae

Final Amount (A)= initial amount (A_o) x (1/2) ^{time taken/half life}

3.5 = 28 x (1/2)^t/30

rearranging, we get

(2) ^-t/30 = 3.5/28=0.125

Taking log₂ both side we get

-t/30= Log₂(0.125)=-3

t=3x30 = 90 years

Therefore the time taken by cesium-137 to reduce to 3.5mg from 28mg would be 90 years