The disintegration rate of a certain radioact | vedclass

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

Question

(C) The disintegration rate $A$ follows the law $A = A_0 e^{-\lambda t}$.At $t = 0$,$A_0 = 4250 \, 	ext{dpm}$.At $t = 10 \, 	ext{min}$,$A = 2250 \,

Vedclass · Accepted Answer

$0.063$

Vedclass · Answer

(C) The disintegration rate $A$ follows the law $A = A_0 e^{-\lambda t}$.At $t = 0$,$A_0 = 4250 \, 	ext{dpm}$.At $t = 10 \, 	ext{min}$,$A = 2250 \, 	ext{dpm}$.Substituting these values into the equation:$2250 = 4250 e^{-\lambda (10)}$$e^{-10\lambda} = \frac{2250}{4250} = \frac{45}{85} = \frac{9}{17}$Taking the natural logarithm on both sides:$-10\lambda = \ln\left(\frac{9}{17}ight)$$10\lambda = \ln\left(\frac{17}{9}ight) \approx \ln(1.888)$$10\lambda \approx 0.6356$$\lambda \approx 0.06356 \, \min^{-1}$.Thus,the approximate decay constant is $0.063 \, \min^{-1}$.

The disintegration rate of a certain radioactive sample at any instant is $4250$ disintegrations per minute. $10$ minutes later,the rate becomes $2250$ disintegrations per minute. The approximate decay constant is $......... \min^{-1}$.

Similar Questions

The half-life of a radioactive element is $30$ days. What percentage of the element will have decayed in $90$ days?

The half-life period of a radioactive element is $10$ days. How long does it take for $90\%$ of a given mass of this element to disintegrate?

The activity of a radioactive sample is measured as $9750$ counts per minute at $t = 0$ and as $975$ counts per minute at $t = 5$ minutes. The decay constant is approximately ............ per minute.

If the undecayed fraction of a radioactive sample is $7/8$ after $6$ days,what will be the undecayed fraction after $10$ days?

The activity of a radioactive sample is $64 \times 10^{-5} \text{ Ci}$. Its half-life is $3 \text{ days}$. The activity will become $5 \times 10^{-6} \text{ Ci}$ after how many days?

Vedclass Test Series

Exam Paper Generator

Online Exam Module