The halflife of a particular element is 410 days What is its

The half-life of a particular element is 410 days. What is its decay constant?

Solution

let initial number of atoms is N0.

let decay constant be lambda.

in that case, at any time, remaining number of atoms is given as N(t)=N0*exp(-lambda*t)

half life is defined as time interval after which number of particle remaining becomes 50% of the original value.

hence N(T)=N0/2 if T=half life

==>N0/2=N0*exp(-lambda*T)

==>1/2=exp(-lambda*T)

==>ln(1/2)=-lambda*T

==>-ln(2)=-lambda*T

==>lambda=ln(2)/T

given that T=410 days= 410*24*3600 seconds=35424000 seconds

==>lambda=ln(2)/T= 0.693/35424000 = 1.956*10^(-8) per second