In a radioactive substance at t = 0,the numbe | vedclass

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

Question

(A) The radioactive decay law is given by $N = N_0 \left( \frac{1}{2} \right)^{t/T}$,where $N_0$ is the initial number of atoms,$N$ is the remaining n

Vedclass · Accepted Answer

$9$

Vedclass · Answer

(A) The radioactive decay law is given by $N = N_0 \left( \frac{1}{2} ight)^{t/T}$,where $N_0$ is the initial number of atoms,$N$ is the remaining number of atoms,$t$ is the time elapsed,and $T$ is the half-life period.Given: $N_0 = 8 	imes 10^4$,$N = 1 	imes 10^4$,and $T = 3 \ years$.Substituting the values into the formula:$1 	imes 10^4 = 8 	imes 10^4 \left( \frac{1}{2} ight)^{t/3}$$\frac{1}{8} = \left( \frac{1}{2} ight)^{t/3}$Since $\frac{1}{8} = \left( \frac{1}{2} ight)^3$,we have:$\left( \frac{1}{2} ight)^3 = \left( \frac{1}{2} ight)^{t/3}$Comparing the exponents:$3 = \frac{t}{3}$$t = 9 \ years$.

In a radioactive substance at $t = 0$,the number of atoms is $8 \times 10^4$. Its half-life period is $3 \ years$. The number of atoms $1 \times 10^4$ will remain after an interval of ........... $years$.

Similar Questions

For a substance,the average life for $\alpha$-emission is $1620$ years and for $\beta$-emission is $405$ years. After how much time will $1/4$ of the material remain after both $\alpha$ and $\beta$ emissions?

If a radioactive substance reduces to $\frac{1}{16}$ of its original mass in $40$ days,what is its half-life in days?

State and derive the law of radioactive decay.

At a given instant,a radioactive sample has $N$ active nuclei. If its decay constant is $\lambda$,which of the following relations is incorrect? (Note: $\lambda$ is very small.)

Half-life of radium is $1620$ years. How many radium nuclei decay in $5$ hours in $5 \, g$ of radium? (Atomic weight of radium $= 223$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module