CBSE Class 12-science Answered

Dear Student

The ans wer is T( R2-R1)

Details fallows

Say there are N0  atoms of radioacctive element  initially.

it is given that it's  mean life time =T

Number of radioactive atoms remained after t time  N(t)  = N0 e^-t/T

Radioactivity at a given time t  R =  dN(t)/dt   = - N(t)/T  (" _ " sign denotes decrease)

R=N0 e^-t/T  / T

R1 = N0 e^-T1/T  / T   ==>e^-T1/T = R1 T /N0 ----------------(1)

R2 = N0 e^-T1/T  / T   ==> e^-T1/T=R2 T/N0-----------------(2)

N(T1)  = N0 e^-T1/T

N(T2)  = N0 e^-T2/T

Number of atoms that have disintegrated in time (T₂ - T₁) is   dN = N(T1) -  N(T2)

=N0( e^-T1/T - e^-T2/T )

Substitute (1),(2) in the above equation

dN=N0 X [  ( T/N0) ( R2-R1) ] = T( R2-R1)

Regards

Team

Topperlearning