The counting rate observed from a radioactive | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The radioactive decay law is given by $A = A_0 \left( \frac{1}{2} \right)^{\frac{t}{T_{1/2}}}$,where $A$ is the activity at time $t$,$A_0$ is the

Vedclass · Accepted Answer

$200$

Vedclass · Answer

(C) The radioactive decay law is given by $A = A_0 \left( \frac{1}{2} ight)^{\frac{t}{T_{1/2}}}$,where $A$ is the activity at time $t$,$A_0$ is the initial activity,and $T_{1/2}$ is the half-life.Given $A_0 = 1600$ counts/sec at $t = 0$ and $A = 100$ counts/sec at $t = 8$ seconds.Substituting these values: $100 = 1600 \left( \frac{1}{2} ight)^{\frac{8}{T_{1/2}}}$.$\frac{100}{1600} = \left( \frac{1}{2} ight)^{\frac{8}{T_{1/2}}} \implies \frac{1}{16} = \left( \frac{1}{2} ight)^{\frac{8}{T_{1/2}}}$.Since $\frac{1}{16} = (\frac{1}{2})^4$,we have $\frac{8}{T_{1/2}} = 4$,which gives $T_{1/2} = 2$ seconds.Now,to find the counting rate at $t = 6$ seconds:$A = 1600 \left( \frac{1}{2} ight)^{\frac{6}{2}} = 1600 \left( \frac{1}{2} ight)^3$.$A = 1600 	imes \frac{1}{8} = 200$ counts/sec.

The counting rate observed from a radioactive source at $t=0$ second was $1600$ counts per second and at $t=8$ seconds it was $100$ counts per second. The counting rate observed,as counts per second at $t=6$ seconds,will be

Similar Questions

Define the average life of a radioactive substance.

An active nucleus decays to one-third $\left(\frac{1}{3}\right)$ of its initial activity in $20 \text{ hours}$. The fraction of original activity remaining after $80 \text{ hours}$ is:

The half-life of radium is $1620$ years and its atomic weight is $226 \ kg/kmol$. The number of atoms that will decay from its $1 \ g$ sample per second will be (Avogadro's number $N_A = 6.02 \times 10^{26} \ atoms/kmol$)

The half-life of a radioactive substance is $T$. The time taken for disintegrating $\frac{7}{8}$th part of its original mass will be

Starting with a sample of pure ${}^{66}Cu$,$\frac{7}{8}$ of it decays into $Zn$ in $15 \ minutes$. The corresponding half-life is .......... $minutes$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module