Question

Fill in the Blank : For a radioactive material, its activity A and rate of change of its activity R are defined as A = dN/dt and R = dA/dt, where N (t) is the number of nuclei at time t. Two radioactive sources P (mean life τ ) and Q (mean life 2τ ) have the same activity at t = 0. Their rates of change of activities at t = 2τ are $R_P$and $R_Q$, respectively. If $R_P/R_Q = n/e$, then the value of n is . .

Answer 1

Answer:

Explanation: Law of radioactivity N = N₀e⁻∧t

where ∧ = decay constant

Activity [A] = [-dN /dt ] = N₀∧e -∧t

Rate of activity R = d [ A] / dt = N₀ ∧²e-∧t

At t =0 , A₁= A₂

NOP∧P = NOQ∧Q

At t = 2τ;

Rp /Rq = {∧p/∧q }² [Nop / Noq]

Mean life  π = 1/∧

Therefore,

Rp / Rq = ∴p/ ∧q e-1

Rp / Rq = n/e

n= 2