Home
Class 12
PHYSICS
Let R(t) represents activity of a sample...

Let `R_(t)` represents activity of a sample at an insant and `N_(t)` represent number of active nuclei in the sample at the instant. `T_(1//2)` represents the half life.
`{:(,"Column I",,"Column II"),((A),t=T_(1//2),(p),R_(t)=(R_(0))/(2)),((B),t=(T_(1//2))/(ln2),(q),N_(0)-N_(t)=(N_(0))/(2)),((C),t=(3)/(2)T_(1//2),(r),(R_(t)-R_(0))/(R_(0)) = (1-e)/(e)),(,,(s),N_(t)=(N_(0))/(2sqrt(2))):}`

Text Solution

Verified by Experts

The correct Answer is:
(A) p,r (B) r (C) s
(A) In half life active sample reduce `=R_(0)/2`
`:.` Decay number of nuclei is `=R_(0)/2`
(B) `N=N_(0)e^(-lambdat)`
where `lambda=` decay constant, `lambda=(ln(2))/t_(1//2)`
`N=N_(0)e^(-(ln2t_(1//2))/(t_(1//2)ln2))implies N=N_(0)/e`
`N_(0)-N=N_(0) [(e-1)/e]implies (N-N_(0))/N_(0) =(1-e)/e`
(C) `N=N_(0)/((2)^(t//T_(1//2)))implies N=N_(0)/2^(3//2)implies N_(0)/(2sqrt(2))`
Promotional Banner

Topper's Solved these Questions

  • SIMPLE HARMONIC MOTION

    ALLEN|Exercise Exercise - 07|2 Videos

  • SIMPLE HARMONIC MOTION

    ALLEN|Exercise Exercise - 08|2 Videos

  • SIMPLE HARMONIC MOTION

    ALLEN|Exercise Exercise - 05|2 Videos

  • RACE

    ALLEN|Exercise Basic Maths (Wave Motion & Dopplers Effect) (Stationary waves & doppler effect, beats)|25 Videos

  • TEST PAPER

    ALLEN|Exercise PHYSICS|4 Videos

Similar Questions

Explore conceptually related problems

The half life of a radioactive substance is T_(0) . At t=0 ,the number of active nuclei are N_(0) . Select the correct alternative.

Radioactivity of a sample at T_(1) time is R_(1) and at time T_(2) is R_(2). If half-life of sample is T, then in time (T_(2)-T_(1)), the number of decayed atoms is proportional to

If S_(n)=sum_(r=0)^(n)(1)/(nC_(r)) and sum_(r=0)^(n)(r)/(nC_(r)), then (t_(n))/(S_(n))=

The radioactivity of sample is R_(1) at a time T_(1) and R_(2) at a time T_(2) . If the half -life of thespeciman is T, the number of atoms that have disintegrated in the time (T_(2)-T_(1)) is equal to :

The radioactivity of a sample is R_(1) at a time T_(1) and R_(2) at a time, T_(2) If the half-line of the secimen is T , the number of atoms that have disintergrated in the time (T_(2) - T_(1)) is proportional to:

Activity of a radioactive substance is R_(1) at time t_(1) and R_(2) at time t_(2) (t_(2) gt t_(1)) then the ratio (R_(2))/( R_(1)) is :

If N_(t) = N_(o)e^(lambdat) then number of disintefrated atoms between t_(1) to t_(2) (t_(2) gt t_(1)) will ve :-

The activity of a radioactive substance is R_(0) at t = 0 , R_(1) at t = t and R_(2) at t = 2t . The decay constant of this species is/are given by:

The radioactivity of a sample is R_(1) at a time T_(1) and R_(2) at time T_(2) . If the half-life of the specimen is T, the number of atoms that have disintegrated in the time (T_(2) -T_(1)) is proporational to