The half-life period of a radioactive substan | vedclass

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

Question

(C) Given that the half-life $T_{1/2} = 60 \ days$.If $\frac{7}{8}$ of the original mass disintegrates,the remaining mass $N$ is $N = N_0 - \frac{7}{8

Vedclass · Accepted Answer

$180$

Vedclass · Answer

(C) Given that the half-life $T_{1/2} = 60 \ days$.If $\frac{7}{8}$ of the original mass disintegrates,the remaining mass $N$ is $N = N_0 - \frac{7}{8}N_0 = \frac{1}{8}N_0$.The relation between remaining mass and initial mass is given by $N = N_0 \left(\frac{1}{2}ight)^n$,where $n$ is the number of half-lives.Substituting the values: $\frac{1}{8}N_0 = N_0 \left(\frac{1}{2}ight)^n$.This simplifies to $\left(\frac{1}{2}ight)^3 = \left(\frac{1}{2}ight)^n$,which gives $n = 3$.The total time taken $t = n 	imes T_{1/2} = 3 	imes 60 \ days = 180 \ days$.

The half-life period of a radioactive substance is $60 \ days$. The time taken for $\frac{7}{8}$ of its original mass to disintegrate will be $...... \ days$.

Similar Questions

The mean life time of a radionuclide,if its activity decreases by $4\%$ for every $1 \ h$,would be .......... $h$ (product is non-radioactive,i.e.,stable).

The half-life of $^{215}At$ is $100 \,\mu s$. After how much time (in $\mu s$) will $1/16^{th}$ of the sample remain undecayed?

The phenomenon of radioactivity is

$A$ radioactive material has an initial amount $16 \, gm$. After $120 \, days$ it reduces to $1 \, gm$. The half-life of the radioactive material is .......... $days$.

The activity of a radioactive sample is $9750$ counts/minute at $t = 0$ and $975$ counts/minute at $t = 5$ minutes. The decay constant is .......... $min^{-1}$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module