Home
Class 12
PHYSICS
Nuclei of radioactive element A are prod...

Nuclei of radioactive element `A` are produced at rate `'t^(2')` (where `t` is time) at any time `t`. The element `A` has decay constant `lambda`. Let `N` be the number of nuclei of element `A` at any time `t`. At time `t=t_(0), dN//dt` is minimum. The number of nuclei of element `A` at time `t=t_(0)` is

A

`(-2t_(0)+lambdat_(0)^(2))/(lambda^(2))`

B

`(t_(0)-lambdat_(0)^(2))/(lambda^(2))`

C

`(2t_(0)+lambdat_(0)^(2))/(lambda)`

D

`(2t_(0)-lambdat_(0)^(2))/(lambda)`

Text Solution

Verified by Experts

The correct Answer is:
A
`(dN)/(dt)=t^(2)-lambdaN rArr(d^(2)N)/(dt^(2))=2t-lambda(dN)/(dt)`
For `(dN)/(dt)` to be min, `(d^(2)N)/(dt^(2))=0`
Promotional Banner

Topper's Solved these Questions

  • NUCLEAR PHYSICS

    NARAYNA|Exercise Level-V Multiple answer questions|45 Videos

  • NUCLEAR PHYSICS

    NARAYNA|Exercise NCERT Based question|72 Videos

  • NUCLEAR PHYSICS

    NARAYNA|Exercise Level-III|38 Videos

  • MOVING CHARGES AND MAGNETISM

    NARAYNA|Exercise EXERCISE - 4|20 Videos

  • NUCLEI

    NARAYNA|Exercise ASSERTION & REASON|5 Videos

Similar Questions

Explore conceptually related problems

Nuclei of a radioactive element A are being produced at a constant rate alpha . The element has a decay constant lambda . At time t=0, there are N_0 nuclei of the element . The number N of nuclei of A at time t is

Nuclei of radioactive element A are being produced at a constant rate. alpha . The element has a decay constant lambda . At time t=0 , there are N_(0) nuclei of the element. (a) Calculate the number N of nuclei of A at time t. (b) IF alpha =2 N_(0) lambda , calculate the number of nuclei of A after one half-life time of A and also the limiting value of N at t rarr oo .

Nuclei of a radioactive element A are being produced at a constant rate alpha . The element has a decay constant lambda . At time t=0 , there are N_0 nuclei of the element. (a) Calculate the number N of nuclei of A at time t. (b) If alpha=2N_0lambda , calculate the number of nuclei of A after one half-life of A, and also the limiting value of N as trarroo .

Nuclei of a radioactive element 'A' are being produced at a constant rate, alpha . The element has a decay constant, lambda . At time, t = 0, there are N_(0) nuclei of the element. If alpha = 4N_(0)lambda , the number of nuclei of A when A has reached steady state:

Nuclei of a radioactive element 'A' are being produced at a constant rate, alpha . The element has a decay constant, lambda . At time, t = 0, there are N_(0) nuclei of the element. If alpha = 2N_(0)lambda the number of nuclei of A after one half life of A becomes

Nuclei of a radioactive A are being produceted at a constant rate a . The electro has a decay constant lambda . At time t = 0 there are N_(0) nucleius of the element . (a) calculate the number N of nuclei of A at same t (b) if a = 2N_(0) lambda) calculate the number of nuclei of A after one half - life of A and the limiting value of N as t rarr oo