The half-life of a radioactive element is 100 | vedclass

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

Question

(C) For a radioactive decay (first-order kinetics),the time taken for $50\%$ decay is $t_{50\%} = 1 	imes t_{1/2} = 100 \, 	ext{min}$.For $87.5\%$ d

Vedclass · Accepted Answer

$200$

Vedclass · Answer

(C) For a radioactive decay (first-order kinetics),the time taken for $50\%$ decay is $t_{50\%} = 1 	imes t_{1/2} = 100 \, 	ext{min}$.For $87.5\%$ decay,the remaining amount is $100\% - 87.5\% = 12.5\%$.Since $12.5\% = (1/2)^3$,this corresponds to $3$ half-lives.Thus,$t_{87.5\%} = 3 	imes t_{1/2} = 3 	imes 100 = 300 \, 	ext{min}$.The time interval between these two stages is $\Delta t = t_{87.5\%} - t_{50\%} = 300 \, 	ext{min} - 100 \, 	ext{min} = 200 \, 	ext{min}$.

The half-life of a radioactive element is $100 \, \text{min}$. The time interval between the stages of $50\%$ and $87.5\%$ decay will be ...... $\text{min}$.

Similar Questions

$A$ radioactive isotope having $t_{1/2} = 3 \ days$ was measured after $12 \ days$. If $3 \ g$ of the isotope remains in the container,what was the initial weight of the isotope (in $g$)?

If the quantity of a radioactive element is doubled,then its rate of disintegration per unit time will be

What is the percentage of a radioactive element decayed after $20 \ s$ if its half-life is $4 \ s$?

$87.5\%$ decomposition of a radioactive substance completes in $3$ hours. What is the half-life of that substance?

$A$ sample is obtained from sea water. $11.9$ $C^{14}$ atoms dissociate from $1 \ g$ of carbon. $15.3$ $C^{14}$ atoms dissociate from a live sample. How many years old is the sample? $(t_{1/2} = 5730 \ \text{years})$

Vedclass Test Series

Exam Paper Generator

Online Exam Module