A radioactive material has a half-life of 8 y | vedclass

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

Question

(D) The radioactive decay law is given by the formula: $\frac{A}{A_0} = (\frac{1}{2})^{t/T_{1/2}}$, where $A$ is the final activity, $A_0$ is the init

Vedclass · Accepted Answer

$24$

Vedclass · Answer

(D) The radioactive decay law is given by the formula: $\frac{A}{A_0} = (\frac{1}{2})^{t/T_{1/2}}$, where $A$ is the final activity, $A_0$ is the initial activity, $t$ is the time elapsed, and $T_{1/2}$ is the half-life.Given that the activity decreases to $1/8$ of its original value, we have $\frac{A}{A_0} = 1/8$.The half-life $T_{1/2} = 8$ years.Substituting these values into the formula: $1/8 = (\frac{1}{2})^{t/8}$.Since $1/8 = (\frac{1}{2})^3$, we can write: $(\frac{1}{2})^3 = (\frac{1}{2})^{t/8}$.Comparing the exponents, we get $3 = t/8$.Therefore, $t = 3 	imes 8 = 24$ years.

$A$ radioactive material has a half-life of $8$ years. The activity of the material will decrease to about $1/8$ of its original value in .......... $years$.

Similar Questions

In a radioactive material,the activity at time $t_{1}$ is $R_{1}$ and at a later time $t_{2}$,it is $R_{2}$. If the decay constant of the material is $\lambda$,then:

$A$ certain radioactive substance has a half-life of $5\, years$. Thus, for a nucleus in a sample of the element, the probability of decay in $10\, years$ is ......... $\%$

The half-life of a radioactive substance is $100 \ s$. How many grams of the radioactive substance will remain after $5 \ min$ if the initial amount is $8 \ g$ (in $g$)?

The specific activity of radium is close to:

There are three lumps of a given radioactive substance. Their activity is in the ratio of $1 : 2 : 3$ now. What will be the ratio of their activities at any further date?

Vedclass Test Series

Exam Paper Generator

Online Exam Module