(C) All nuclear decays follow first-order kinetics.$t = \frac{1}{k} \ln \frac{[A_0]}{[A]}$Given $t_{1/2} = 6.93 \; \text{years}$,so $k = \frac{0.693}{

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

(C) All nuclear decays follow first-order kinetics.$t = \frac{1}{k} \ln \frac{[A_0]}{[A]}$Given $t_{1/2} = 6.93 \; \text{years}$,so $k = \frac{0.693}{t_{1/2}} = \frac{0.693}{6.93} = 0.1 \; \text{year}^{-1}$.To reduce it by $90 \%$,the remaining amount $[A] = 10 \% \text{ of } [A_0] = 0.1 [A_0]$.$t = \frac{2.303}{k} \log_{10} \frac{[A_0]}{0.1 [A_0]} = \frac{2.303}{0.1} \log_{10} (10) = 23.03 \times 1 = 23.03 \; \text{years}$.

Class 12 Chemistry Nuclear Chemistry Rate of decay and Half-life

During a nuclear explosion,one of the products is $^{90}Sr$ with a half-life of $6.93 \; \text{years}$. If $1 \; \mu g$ of $^{90}Sr$ was absorbed in the bones of a newly born baby in place of $Ca$,how much time,in years,is required to reduce it by $90 \%$ if it is not lost metabolically?

JEE MAIN 2020 All JEE MAIN

A
$27.01$
B
$25.07$
C
$23.03$
D
$21.06$

Explore More

Browse All

Question Bank

All Subjects

Class 12 Questions

Class 12

Chemistry Questions

Chapter

Nuclear Chemistry

Subtopic

Rate of decay and Half-life

Previous Year

JEE MAIN 2020 Paper All JEE MAIN years →

Radioactive lead $_{82}Pb^{201}$ has a half-life of $8 \ hours$. Starting from $1 \ mg$ of this isotope,how much will remain after $24 \ hours$?

Medium

View Solution

The radium and uranium atoms in a sample of uranium mineral are in the ratio of $1 : 2.8 \times 10^6$. If the half-life period of radium is $1620$ years,the half-life period of uranium will be:

Difficult

View Solution

In a radioactive decay,a uranium atom transforms into a lead atom. If a rock sample from the moon contains an equal number of uranium and lead atoms,and the half-life $(t_{1/2})$ for uranium is $4.5 \times 10^9$ years,then the age of the rock will be:

Medium

View Solution

The half-life period of a radioactive substance is $140 \ days$. After how much time will $15 \ g$ decay from a $16 \ g$ sample of it?

Medium

View Solution

The number of $\alpha$-particles emitted per second by a radioactive element falls to $1/32$ of its original value in $50 \ days$. The half-life period of this element is .......... $days$.

Medium

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

During a nuclear explosion,one of the products is $^{90}Sr$ with a half-life of $6.93 \; \text{years}$. If $1 \; \mu g$ of $^{90}Sr$ was absorbed in the bones of a newly born baby in place of $Ca$,how much time,in years,is required to reduce it by $90 \%$ if it is not lost metabolically?

Similar Questions

Radioactive lead $_{82}Pb^{201}$ has a half-life of $8 \ hours$. Starting from $1 \ mg$ of this isotope,how much will remain after $24 \ hours$?

The radium and uranium atoms in a sample of uranium mineral are in the ratio of $1 : 2.8 \times 10^6$. If the half-life period of radium is $1620$ years,the half-life period of uranium will be:

In a radioactive decay,a uranium atom transforms into a lead atom. If a rock sample from the moon contains an equal number of uranium and lead atoms,and the half-life $(t_{1/2})$ for uranium is $4.5 \times 10^9$ years,then the age of the rock will be:

The half-life period of a radioactive substance is $140 \ days$. After how much time will $15 \ g$ decay from a $16 \ g$ sample of it?

The number of $\alpha$-particles emitted per second by a radioactive element falls to $1/32$ of its original value in $50 \ days$. The half-life period of this element is .......... $days$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module