The half-life of radium-226 is 1620 years. Th | vedclass

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

Question

(D) Given initial amount $N_o = 10 \ g$,final amount $N = 1.25 \ g$,and half-life $t_{1/2} = 1620 \ years$. Using the radioactive decay formula: $N =

Vedclass · Accepted Answer

$4860$

Vedclass · Answer

(D) Given initial amount $N_o = 10 \ g$,final amount $N = 1.25 \ g$,and half-life $t_{1/2} = 1620 \ years$. Using the radioactive decay formula: $N = N_o (1/2)^n$,where $n$ is the number of half-lives $(n = t / t_{1/2})$. Substituting the values: $1.25 = 10 	imes (1/2)^n$. $1.25 / 10 = (1/2)^n \implies 0.125 = (1/2)^n \implies 1/8 = (1/2)^n$. Since $1/8 = (1/2)^3$,we get $n = 3$. Now,calculating the total time: $t = n 	imes t_{1/2} = 3 	imes 1620 = 4860 \ years$.

The half-life of radium-$226$ is $1620$ years. The time taken to convert $10 \ g$ of radium to $1.25 \ g$ is ......... years.

Similar Questions

The half-lives of two radioactive nuclides $A$ and $B$ are $1 \ min$ and $2 \ min$ respectively. Equal weights of $A$ and $B$ are taken separately and allowed to disintegrate for $4 \ min$. What will be the ratio of weights of $A$ and $B$ disintegrated?

The half-life of radioactive $C^{14}$ is $5760 \ years$. In how many years will a $200 \ mg$ sample of $C^{14}$ be reduced to $25 \ mg$?

$C-14$ is used in carbon dating of dead objects because

In the case of a radioisotope,the value of $T_{1/2}$ and $\lambda$ are identical in magnitude. The value is

If $8.0 \ g$ of a radioactive isotope has a half-life of $10 \ hrs$. The half-life of $2.0 \ g$ of the same substance is ...... $hrs$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module