The half-life of C^{14} is 5760 years. For a | vedclass

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

Question

(D) Given: Half-life of $C^{14}$, $t_{1/2} = 5760 \ years$. Initial amount, $N_0 = 200 \ mg$. Final amount, $N_t = 25 \ mg$. Radioactive decay follows

Vedclass · Accepted Answer

$17280$

Vedclass · Answer

(D) Given: Half-life of $C^{14}$, $t_{1/2} = 5760 \ years$. Initial amount, $N_0 = 200 \ mg$. Final amount, $N_t = 25 \ mg$. Radioactive decay follows first-order kinetics. We can use the relation: $N_t = N_0 	imes (1/2)^n$, where $n$ is the number of half-lives. $25 = 200 	imes (1/2)^n$ $1/8 = (1/2)^n$ $(1/2)^3 = (1/2)^n$ Therefore, $n = 3$. Total time $t = n 	imes t_{1/2} = 3 	imes 5760 \ years = 17280 \ years$. Alternatively, as shown in the diagram: $200 \ mg$ $\xrightarrow{t_{1/2}} 100 \ mg$ $\xrightarrow{t_{1/2}} 50 \ mg$ $\xrightarrow{t_{1/2}} 25 \ mg$. Total time = $3 	imes 5760 \ years = 17280 \ years$.

The half-life of $C^{14}$ is $5760 \ years$. For a $200 \ mg$ sample of $C^{14}$, the time taken to change to $25 \ mg$ is (in $years$)

Similar Questions

The order of a radioactive disintegration reaction is:

Radioactive lead $_{82}Pb^{201}$ has a half-life of $8 \ hours$. Starting from $1 \ mg$ of this isotope,how much will remain after $24 \ hours$?

$A$ first-order nuclear reaction is half-completed in $45 \ minutes$. How long does it take for $99.9\%$ of the reaction to be completed in $hours$?

The half-life of a radionuclide is $69.3 \text{ minutes}$. What is its average life (in minutes)?

$10 \ g$ of a radioactive element is disintegrated to $1 \ g$ in $2.303 \ \text{minutes}$. What is the half-life (in minutes) of that radioactive element?

Vedclass Test Series

Exam Paper Generator

Online Exam Module