The half-life of a radioactive substance is 1 | vedclass

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

Question

(D) The number of undecayed atoms $N$ after time $t$ is given by $N = N_0 \left(\frac{1}{2}ight)^{\frac{t}{T_{1/2}}}$,where $T_{1/2} = 18 	ext{ min

Vedclass · Accepted Answer

$36$

Vedclass · Answer

(D) The number of undecayed atoms $N$ after time $t$ is given by $N = N_0 \left(\frac{1}{2}ight)^{\frac{t}{T_{1/2}}}$,where $T_{1/2} = 18 	ext{ min}$.For $20 \%$ decay,the remaining amount is $N_1 = N_0 - 0.20 N_0 = 0.8 N_0$.Thus,$0.8 N_0 = N_0 \left(\frac{1}{2}ight)^{\frac{t_1}{18}} \implies \left(\frac{1}{2}ight)^{\frac{t_1}{18}} = 0.8 \quad (i)$.For $80 \%$ decay,the remaining amount is $N_2 = N_0 - 0.80 N_0 = 0.2 N_0$.Thus,$0.2 N_0 = N_0 \left(\frac{1}{2}ight)^{\frac{t_2}{18}} \implies \left(\frac{1}{2}ight)^{\frac{t_2}{18}} = 0.2 \quad (ii)$.Dividing equation $(i)$ by $(ii)$:$\frac{(1/2)^{t_1/18}}{(1/2)^{t_2/18}} = \frac{0.8}{0.2} = 4$.$\left(\frac{1}{2}ight)^{\frac{t_1-t_2}{18}} = 4 = 2^2 = \left(\frac{1}{2}ight)^{-2}$.Equating the exponents: $\frac{t_1-t_2}{18} = -2 \implies t_2 - t_1 = 36 	ext{ min}$.

The half-life of a radioactive substance is $18 \text{ minutes}$. The time interval between its $20 \%$ decay and $80 \%$ decay in minutes is

Similar Questions

From $N$ atoms of a radioactive element,$n$ alpha particles are emitted per second. The half-life of the element is ......

Two radioactive samples $A_1$ and $A_2$ have decay constants $10\lambda_0$ and $\lambda_0$ respectively. If they initially contain the same number of nuclei,find the ratio of the number of undecayed nuclei after time $t = 1/(9\lambda_0)$.

Mean life of a radioactive sample is $100$ seconds. Then its half-life (in minutes) is

The decay constant of a radioisotope is $\lambda$. If its activity at times $t_1$ and $t_2$ are $A_1$ and $A_2$ respectively,then the number of nuclei that have decayed during the time interval $(t_1 - t_2)$ is:

In an old rock,the ratio of uranium to lead nuclei is $1:1$. The half-life of uranium is $4.5 \times 10^9$ years. If the rock initially contained only uranium nuclei,how old is the rock?

Vedclass Test Series

Exam Paper Generator

Online Exam Module