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

At time t=0, a container has N0 radioactive atoms with a decay constant λ. In addition, C numbers of atoms of the same type are being added to the container per unit time. How many atoms of this type are there at t=T ?

A
CλeλTN0eλT
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
CλeλT+N0eλT
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
Cλ(1eλT)+N0eλT
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
Cλ(1+eλT)+N0eλT
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C Cλ(1eλT)+N0eλT
At t=0 initial nucleon =N0
Additionally, at a constant rate (λNC)
=dNdt
t0dt=NN0(dNλNC)
t=1λln(λNC)NN0
t=1λln(λNCλN0C)
eλt=λNCλN0C
λNC=eλt(λN0C)
N=Cλ+eλtλ(λN0C)
=Cλ+N0eλtCλeλt
=Cλ[1e(λt)]+N0eλt
At t=TN=Cλ[1e(λT)]+N0eλT

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