Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Medical
  • Nucleus of a radioactive element are being produced at constant rate and

Nucleus of a radioactive element \mathrm{X} are being produced at constant rate \mathrm{K} and this element decays to a stable nucleus Y with a decay constant \lambda and half life \mathrm{T}_{1 / 2} . At time t=0, there are \mathrm{N}_0 nuclei of the element X. The number \mathrm{N}_{\mathrm{X}} of nuclei of X at time \mathrm{t}=\mathrm{T}_{1 / 2}  is

Option: 1

\frac{\mathrm{K}+\lambda \mathrm{N}_0}{2 \lambda}


Option: 2

\left(2 \lambda \mathrm{N}_0-\mathrm{K}\right) \frac{1}{\lambda}


Option: 3

\left[\lambda \mathrm{N}_0+\frac{\mathrm{K}}{2}\right] \frac{1}{\lambda}


Option: 4

Data is insufficient.


Answers (1)

best_answer

\frac{\mathrm{dN}_{\mathrm{X}}}{\mathrm{dt}}=\mathrm{K}-\lambda \mathrm{N}_{\mathrm{X}}

                N_X=\frac{1}{\lambda}\left[K-\left(K-\lambda N_0\right) e^{-\lambda t}\right]

\text { at time } \mathrm{t}=\mathrm{T}_{1 / 2}, e^{-\lambda t}=1 / 2

Posted by

Gaurav

View full answer

NEET 2024 Most scoring concepts

    Just Study 32% of the NEET syllabus and Score up to 100% marks

Similar Questions

Trending Articles/News

anam-khan

AFMC hikes MBBS seat leaving bond penalty, mandates 7 years of commission service
anam-khan

‘Patience and not backing down’: Kabir Paharia’s SC fight eases MBBS admissions for disabled candidates
anam-khan

SC wants to know if FIRs filed over suicides of IIT student, NEET aspirant

Latest Question