Answer to Question #85018 in Physics for akash singh

Question

The disintegration constant of U 238 is 4.87*10^-18 s^-1. Calculate its half-life (in
years). Also calculate the number of disintegration per second from 1 gram of
Uranium. It is given that Avogadro’s number = 6.02 × 10^23

Answer 1

The half-life

T_(1/2)=ln⁡2/λ=ln⁡2/(4.87×〖10〗^(-18) s^(-1) )=1.42 s=4.51×〖10〗^9 years

The number of disintegration per second

-dN/dt=λN

Since

N=N_A m/M

So

-dN/dt=λN_A m/M

-dN/dt=4.87×〖10〗^(-18)×6.02×〖10〗^23×1/238=1.23×〖10〗^4