Nuclei of a radioactive element A are being produced at a constant rate α. The element has a decay constant λ. At time t = 0, there are N 0 nuclei of the element

Question

Navjyot Kalra · Answer

Hello Student,

Please find the answer to your question

(a) Let at time ‘t’ number of radioactive are N.

Net rate of formation of nuclei of A.

dN /dt = α – λ N or dN / α – λN = dt

or $\int_{N_0}^{N}\frac{dN}{\alpha - \lambda N } = \int_{0}^{t} dt$

Solving this equation, we get

N = 1 / λ [α – (α – λN₀)e^-λt] …..(1)

(b) Substituting α = 2λN₀ and

t = t_1/2 = 1n(2) / λ in equation (1),

we get, N = 3/2 N₀

(ii) Substituting α = 2λ N₀ and t ⟶ ∞ in equation (1), we get

N = α / λ = 2 N₀

Thanks
Navjot Kalra
askIITians Faculty

Thank you for registering.

Register Now and Win Upto 25% Scholorship for a Full Academic Year !

Enter Your Details

Registration done!

Guest

Nuclei of a radioactive element A are being produced at a constant rate α. The element has a decay constant λ. At time t = 0, there are N 0 nuclei of the element

Nuclei of a radioactive element A are being produced at a constant rate α. The element has a decay constant λ. At time t = 0, there are N₀ nuclei of the element

1 Answers

Think You Can Provide A Better Answer ?

Other Related Questions on Modern Physics

ASK QUESTION

Answer and earn gift vouchers

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Complete Self Study Package designed by Industry Leading Experts

Live 1-1 coding classes to unleash the Creator in your Child

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Register Now & Win Upto 25% Scholorship

Thank you for registering.

Register Now and Win Upto 25% Scholorship for a Full Academic Year !

Enter Your Details

Registration done!

Guest

IIT JEE Courses

One Year IIT Programme

Two Year IIT Programme

Crash Course

NEET Courses

One Year NEET Programme

Two Year NEET Programme

One to One

School Board

Live Online classes

Class 11 & 12

Class 9 & 10

Class 6, 7 & 8

Test Series

JEE test series

NEET test series

C.B.S.E test series

Complete Self Study Packages

FULL COURSE

For class 12th

For class 11th

Nuclei of a radioactive element A are being produced at a constant rate α. The element has a decay constant λ. At time t = 0, there are N 0 nuclei of the element

Nuclei of a radioactive element A are being produced at a constant rate α. The element has a decay constant λ. At time t = 0, there are N0 nuclei of the element

1 Answers

Think You Can Provide A Better Answer ?

Other Related Questions on Modern Physics

ASK QUESTION

Answer and earn gift vouchers

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Complete Self Study Package designed by Industry Leading Experts

Live 1-1 coding classes to unleash the Creator in your Child

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Register Now & Win Upto 25% Scholorship

Nuclei of a radioactive element A are being produced at a constant rate α. The element has a decay constant λ. At time t = 0, there are N₀ nuclei of the element