Assertion : If the half-life of a radioactive | vedclass

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

Question

(D) The half-life $(T_{1/2})$ of the radioactive substance is $40 \ days$. The amount of substance remaining after time $t$ is given by $N = N_0 \left

Vedclass · Accepted Answer

If the Assertion is incorrect but the Reason is correct.

Vedclass · Answer

(D) The half-life $(T_{1/2})$ of the radioactive substance is $40 \ days$. The amount of substance remaining after time $t$ is given by $N = N_0 \left( \frac{1}{2} ight)^{t/T_{1/2}}$.For $t = 20 \ days$,the number of half-lives is $n = \frac{20}{40} = 0.5$.The amount remaining is $N = N_0 \left( \frac{1}{2} ight)^{0.5} = N_0 \left( \frac{1}{\sqrt{2}} ight) \approx 0.707 N_0$.The amount decayed is $N_0 - N = N_0 - 0.707 N_0 = 0.293 N_0$,which is $29.3\%$.Since $29.3\% 
eq 25\%$,the Assertion is incorrect.The formula provided in the Reason is the standard law of radioactive decay,which is correct.Therefore,the Assertion is incorrect but the Reason is correct.

Assertion : If the half-life of a radioactive substance is $40 \ days$,then $25\%$ of the substance decays in $20 \ days$.
Reason : $N = N_0 \left( \frac{1}{2} \right)^n$,where $n = \frac{\text{time elapsed}}{\text{half-life period}}$.

Similar Questions

$A$ radioactive element emits $200$ particles per second. After $3$ hours,$25$ particles per second are emitted. The half-life period of the element will be .......... $minutes$.

The initial activity of a radioactive element is $1600$. After $t = 8 \, s$,the activity becomes $100$. What is the activity at $t = 6 \, s$?

$A$ radioactive material of half-life $2.5$ hours emits radiation that is $32$ times the safe maximum level. The time (in hours) after which the material can be handled safely is

Radioactive material $A$ has decay constant $8 \lambda$ and material $B$ has decay constant $\lambda$. Initially,they have the same number of nuclei. After what time will the ratio of the number of nuclei of material $B$ to that of $A$ be $\frac{1}{e}$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module

Assertion : If the half-life of a radioactive substance is $40 \ days$,then $25\%$ of the substance decays in $20 \ days$.Reason : $N = N_0 \left( \frac{1}{2} \right)^n$,where $n = \frac{\text{time elapsed}}{\text{half-life period}}$.