The half life of a radioactive substance...

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.

The number of nuclel decayed in time internal `0-t'` is `N_(0)e^(-lambdat)`

The number of nuclel decayed in time internal `0-t'` is `N_(0)(1-e^(-lambdat))`

The probability that a radioactive nuclel does not decay I inteval `0-t` is `e^(-lambdat)`

The probability that a radioactive nuclel does not decay I inteval `1-e^(-lambdat)`

Text Solution

Verified by Experts

The correct Answer is:

B, C

At `t = 0, N_(1) = N_(0)`
At time `t : N_(2) = N_(0)e^(-lambdat)`
Decayed in time `t (N_(1) - N_(2)) = N_(0)(1-e^(-lambdat))`
Porbability that a radioactive nuclei does not decay in `t = 0` to `t : (N)/(N_(0)) = (N_(0)e^(-lambdat))/(N_(0)) = e^(-lambdat)`

Topper's Solved these Questions

SIMPLE HARMONIC MOTION
ALLEN|Exercise Exercise - 14|2 Videos
SIMPLE HARMONIC MOTION
ALLEN|Exercise Exercise - 15|2 Videos
SIMPLE HARMONIC MOTION
ALLEN|Exercise Exercise - 12|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

Half life of a radioactive substance A is two times the half life of another radioactive substance B. Initially, the number of nuclei of A and B are N_(A) and N_(B) respectively. After three half lives of A, number of nuclei of both are equal. Then the ratio (N_(A))/(N _(B)) is

`(1)/(3)`

`(1)/(6)`

`(1)/(8)`

`(1)/(4)`

The half life of radioactive substance is T. Then the fraction of the substance that has decayed in time t is-

(t/T)

`2^(t//T)`

`(1//2)^(t//T)`

`1-(1//2)^(t//T)`

The count rate of a radioactive sample was 1600 count/s at t=0 and 100 counts at t=8 s . Select the correct alternatives

Its count rate was 200 counts at t=6 s

Its count rate was 200 counts at t=4 s

Half life of the sample is 4s

Mean life of the sample is 2.88 s