The half-life of a radioactive isotope x is 5 | vedclass

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

Question

(A) Let $N_x$ be the amount of radioactive isotope $x$ and $N_y$ be the amount of stable element $y$ present in the rock.The ratio is given as $N_x :

Vedclass · Accepted Answer

$150$

Vedclass · Answer

(A) Let $N_x$ be the amount of radioactive isotope $x$ and $N_y$ be the amount of stable element $y$ present in the rock.The ratio is given as $N_x : N_y = 1 : 7$.The initial amount of the radioactive isotope $N_0$ is the sum of the remaining isotope and the decayed product:$N_0 = N_x + N_y = 1 + 7 = 8$.We know that $N_x = N_0 	imes (1/2)^n$, where $n$ is the number of half-lives.$1 = 8 	imes (1/2)^n \Rightarrow (1/2)^n = 1/8 = (1/2)^3$.Thus, $n = 3$.The age of the rock $t$ is given by $t = n 	imes T_{1/2}$, where $T_{1/2} = 50$ years.$t = 3 	imes 50 = 150$ $years$.

The half-life of a radioactive isotope $x$ is $50$ years. It decays to another element $y$ which is stable. The two elements $x$ and $y$ were found to be in the ratio of $1 : 7$ in a sample of a given rock. The age of the rock was estimated to be ........... $years$.

Similar Questions

The masses of two radioactive substances are same and their half-lives are $1 \ yr$ and $2 \ yr$ respectively. The ratio of their activities after $4 \ yr$ will be

If the half-life of a radioactive element is $12.5 \ h$,then the time taken to disintegrate $256 \ g$ of the substance into $1 \ g$ is (in hours)

Two radioactive substances $A$ and $B$ have decay constants $5\lambda$ and $\lambda$ respectively. At $t = 0$,a sample has the same number of the two nuclei. The time taken for the ratio of the number of nuclei to become $(1/e)^2$ will be

The mean life of a radioactive material for alpha decay and beta decay are,respectively,$1620$ years and $520$ years. What is the half life of the sample (in years)?

Find the time in years required for $10\%$ of a radioactive sample to decay,given that its half-life is $22 \text{ years}$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module