The radioactivity of a given sample of whisky | vedclass

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

Question

(D) The activity $A$ at time $t$ is given by $A = A_0 (1/2)^n$, where $n$ is the number of half-lives.Given that the activity is $3\%$ of the original

Vedclass · Accepted Answer

$70 	ext{ years}$ back

Vedclass · Answer

(D) The activity $A$ at time $t$ is given by $A = A_0 (1/2)^n$, where $n$ is the number of half-lives.Given that the activity is $3\%$ of the original, we have $0.03 = (1/2)^n$.Taking the logarithm, $\ln(0.03) = n \ln(0.5)$, which gives $n = \ln(0.03) / \ln(0.5) \approx 5.06$.Thus, the time elapsed for the tritium decay is $t = n 	imes T_{1/2} = 5.06 	imes 12.5 	ext{ years} \approx 63.25 	ext{ years}$.Since the reference bottle was already $7 	ext{ years}$ old, the total age of the sample is $63.25 + 7 \approx 70.25 	ext{ years}$.Therefore, the sample was prepared about $70 	ext{ years}$ back.

The radioactivity of a given sample of whisky due to tritium (half-life $12.5 \text{ years}$) was found to be only $3\%$ of that measured in a recently purchased bottle marked "$7 \text{ years}$ old". The sample must have been prepared about:

Similar Questions

Which sample,$A$ or $B$ shown in the figure,has a shorter mean-life?

Consider a radioactive material of half-life $1.0 \, \text{minute}$. If one of the nuclei decays now,the next one will decay

$A$ radioactive substance has a half-life of $60 \text{ minutes}$. During $3 \text{ hours}$,the amount of substance decayed would be: (in $\%$)

Half lives of two radioactive substances $A$ and $B$ are respectively $20$ minutes and $40$ minutes. Initially,the sample of $A$ and $B$ have equal number of nuclei. After $80$ minutes,the ratio of the remaining numbers of $A$ and $B$ nuclei is

The unit of radioactivity is Rutherford. Its value is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module