Question

The half-life of a radioactive substance is 100 years. Calculate in how many years the activity will decay to `1//10^(th)` of its initial value.

Answer 1

T = 100 years
`(N)/(N_(0))=(1)/(10), t = ?`
`lambda = (0.693)/(T)=(0.693)/(100)=0.693xx10^(-2)` years
`N=N_(0)e^(-lambda t)rArr e^(-lambda t)=(N)/(N_(0))=(1)/(10)`
`e^(lambda t)=10 rArr lambda t = log_(e )^(10)=2.303xxlog_(10)^(10)`
`t=(2.303xx1)/(0.693xx10^(-2))=3.323xx10^(2)`
`= 332.2` years