A and B are two radioactive substances whose | vedclass

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

Question

(A) The amount of a radioactive substance remaining after time $t$ is given by $N = N_0 \left( \frac{1}{2} \right)^{t/T_{1/2}}$.For substance $A$: $N_

Vedclass · Accepted Answer

$6.62$

Vedclass · Answer

(A) The amount of a radioactive substance remaining after time $t$ is given by $N = N_0 \left( \frac{1}{2} ight)^{t/T_{1/2}}$.For substance $A$: $N_A = 10 \left( \frac{1}{2} ight)^{t/1}$.For substance $B$: $N_B = 1 \left( \frac{1}{2} ight)^{t/2}$.Given that the remaining quantities are equal, $N_A = N_B$.$10 \left( \frac{1}{2} ight)^t = 1 \left( \frac{1}{2} ight)^{t/2}$.$10 = \frac{(1/2)^{t/2}}{(1/2)^t} = (1/2)^{-t/2} = 2^{t/2}$.Taking the logarithm on both sides: $\log_{10}(10) = \frac{t}{2} \log_{10}(2)$.$1 = \frac{t}{2} 	imes 0.3010$.$t = \frac{2}{0.3010} \approx 6.64 \, years$. (Rounding to the nearest provided option, $6.62$).

$A$ and $B$ are two radioactive substances whose half-lives are $1$ and $2$ years respectively. Initially, $10 \, g$ of $A$ and $1 \, g$ of $B$ are taken. The time (approximate) after which they will have the same quantity remaining is ........... $years$.

Similar Questions

The half-life of a radioactive nucleus is $50$ days. The time interval $(t_2 - t_1)$ between the time $t_2$ when $\frac{2}{3}$ of it had decayed and the time $t_1$ when $\frac{1}{3}$ of it had decayed is (in days):

The half-life of polonium is $140 \, days$. After how many days will $16 \, g$ of polonium be reduced to $1 \, g$ (or $15 \, g$ will decay)?

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

The half-life of $Bi^{210}$ is $5 \ days$. What time is taken by $(7/8)^{th}$ part of the sample to decay?

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module