Home
Class 12
PHYSICS
A radioactive isotope is being produced ...

A radioactive isotope is being produced at a constant rate `dN//dt=R` in an experiment. The isotope has a half-life `t_(1//2)`.Show that after a time `t gtgt t_(1//2)`,the number of active nuclei will become constant. Find the value of this constant.

A

`RT`

B

`R/T1n2`

C

`RT 1n2`

D

`(RT)/(1n2)`

Text Solution

Verified by Experts

The correct Answer is:
D
When the rate producion = rate of disintegration, number of nuclei or maximum.
`:.` `lambdaN=A`
or `(1n2)/TN=A` or `N=(AT)/(1n2)=`maximum
Promotional Banner

Topper's Solved these Questions

  • MODERN PHYSICS - 2

    DC PANDEY|Exercise Level 2 More Than One Correct|6 Videos

  • MODERN PHYSICS - 2

    DC PANDEY|Exercise Level 2 Comprehension Based|3 Videos

  • MODERN PHYSICS - 2

    DC PANDEY|Exercise Level 1 Subjective Questions|1 Videos

  • MODERN PHYSICS - 1

    DC PANDEY|Exercise Level 2 Subjective|23 Videos

  • NUCLEI

    DC PANDEY|Exercise C MADICAL ENTRANCES GALLERY|46 Videos

Similar Questions

Explore conceptually related problems

A radiaocatice isotope is being produced at a constant rate X . Half-life of the radioactive substance is Y . After some time, the number of radioactive nuceli become constant. The value of this constant is .

A radioactive isotopes is being produced at a constant rate X. Half life of substance is Y . After some time the no of radioactive nuclei become constant. The value of constant is

A radioactive nucleus is being produced at a constant rate alpha per second. Its decay constant is lamda . If N_0 are the number of nuclei at time t = 0 , then maximum number of nuclei possible are.

Nuclei of a radioactive element X are being produced at a constant rate K and this element decays to a stable nucleus Y with a decay constant lambda and half-life T_(1//3) . At the time t=0 , there are N_(0) nuclei of the element X. The number N_(Y) of nuclei of Y at time t is .

Radioactive isotopes are produced in a nuclear physics experiment at a constant rate dN//dt=R .An inductor of inductance 100 mH, a resistor of resistance 100 Omega and a battery are connected to form a series circuit.the circuit is switched on at the instant the production of radioactive isotope starts. It is found that i//N remains constant in time where i is the current in the circuit at time t and N is the number of active nuclei at time t. Find the half-life of the isotope.

Nuclei of a radioactive element X are being produced at a constant rate K and this element decays to a stable nucleus Y with a decay constant lambda and half-life T_(1//3) . At the time t=0 , there are N_(0) nuclei of the element X . The number N_(X) of nuclei of X at time t=T_(1//2) is .

Nuclei of a radioactive element X are being produced at a constant rate K and this element decays to a stable nucleus Y with a decay constant lambda and half-life T_(1//3) . At the time t=0 , there are N_(0) nuclei of the element X . The number N_(Y) of nuclei of Y at t=T_(1//2) is.