wiz-icon
MyQuestionIcon
MyQuestionIcon
7
You visited us 7 times! Enjoying our articles? Unlock Full Access!
Question

Nuclei of a radioactive element is produced at constant rate α and they decay with decay constant λ. At t=0, the number of nuclei is 0. The number of active nuclei at time t is

A
αλ(1eλt)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
α(1eλt)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
αλeλt
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
αeλt
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A αλ(1eλt)
According to the information,
dNdt=λN+α
Rearranging and integrating,
N0dNλN+α=t0dt

Let λN+α=p
λdN=dp
dN=dpλ

Substituting back in integral,
pαdpp=t0λdt
This gives p=αeλt
Putting the expression for p, we get
p=λN+α=αeλt
This gives
N=αλ(1eλt)


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon