# The decay constant of a radioisotope is $\lambda$ . if $A_{1}$ and $A_{2}$ are its activities at times $t_{1}$ and $t_{2}$ respectively, the number of nuclei which have decayed during the time$\left ( t_{1} \right-_{t_{2}} )$ : Option 1) $\lambda \left ( A_{1} \right-A_{2} )$ Option 2) $A_{1}t_{1}-A_{2}t_{2}$ Option 3) $A_{1}-A_{2}$ Option 4) $\left ( A_{1} \right-A_{2} )/\lambda$

As we learnt in

Number of nuclei after disintegration -

$N=N_{0}e^{-\lambda t}$ or $A=A_{0}e^{-\lambda t}$

- wherein

Number of nucleor activity at a time is exponentional function

$-\frac{dN}{dt}= \lambda N$

- wherein

Ratio of disintegration is propotional to number of nuclei

$\lambda$= disintegration constant

$A_{1}=A_{o}\cdot e^{-\lambda t_{1}} \: \: \Rightarrow N_{1}=\frac{A_{1}}{\lambda }=\frac{A_{o}}{\lambda }\cdot e^{-\lambda t_{2}}$

$A_{2}=A_{o}\cdot e^{-\lambda t_{2}} \: \: \Rightarrow N_{2}=\frac{A_{2}}{\lambda }=\frac{A_{o}}{\lambda }\cdot e^{-\lambda t_{1}}$

Number of nuclei decayed between t1 and t2 = N1-N2= $\frac{A_{1}-A_{2}}{\lambda }$

Option 1)

$\lambda \left ( A_{1} \right-A_{2} )$

Incorrect

Option 2)

$A_{1}t_{1}-A_{2}t_{2}$

Incorrect

Option 3)

$A_{1}-A_{2}$

Incorrect

Option 4)

$\left ( A_{1} \right-A_{2} )/\lambda$

Correct

### Preparation Products

##### Rank Booster NEET 2021

This course will help student to be better prepared and study in the right direction for NEET..

₹ 13999/- ₹ 9999/-
##### Knockout NEET May 2021 (Subscription)

An exhaustive E-learning program for the complete preparation of NEET..

₹ 4999/-
##### Knockout NEET May 2022 (Subscription)

An exhaustive E-learning program for the complete preparation of NEET..

₹ 5499/-
##### Knockout NEET May 2021

An exhaustive E-learning program for the complete preparation of NEET..

₹ 22999/- ₹ 14999/-