wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

A radioactive nuclide is produced at the constant rate of n per second. It decays into a stable nucleus with decay constant λ. If N0 is a number of nuclei at t=0, then expected number N of nuclei in existence after t seconds is given by

A
N=nλ+N0eλt
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
N=N0eλt
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
N=nλ+(N0+nλ)eλt
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
N=nλ+(N0nλ)eλt
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D N=nλ+(N0nλ)eλt
The population is increasing by n and simultaneously decreasing by λN.

dNdt=nλN

Integrating the above equation within proper limit,

NN0dNnλN=t0dt

1λ[ln(nλN)ln(nλN0)]=t

ln[nλNnλN0]=λt

nλNnλN0=eλt

nλN=(nλN0)eλt

nneλt+λN0eλt=λN

N=nλ[1eλt]+N0eλt

N=nλ+(Nonλ)eλt

Hence, (D) is the correct answer.

flag
Suggest Corrections
thumbs-up
1
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Alpha Decay
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon