NEET-XII-Physics
46: The Nucleus
- #23A certain sample of a radioactive material decays at the rate of 500 per second at a certain time. The count rate falls to 200 per second after 50 minutes. (a) What is the decay constant of the sample? (b) What is its half-life? (a) What is the decay constant of the sample? (b) What is its half-life?Ans : Given:
Initial rate of decay, A0 = 500,
Rate of decay after 50 minutes, A = 200
Time, t = 50 min
= 50 `` \times `` 60
= 3000 s (a) Activity, A = A0e-λt
Here, `` \lambda `` = Disintegration constant
`` \therefore `` 200 = 500 × e-50×60×λ
`` \Rightarrow \frac{2}{5}={e}^{-3000\lambda }``
`` \Rightarrow \,\mathrm{\,In\,}\frac{2}{5}=-3000\lambda ``
`` \Rightarrow \lambda =3.05\times {10}^{-4}{\,\mathrm{\,s\,}}^{-1}``
`` `` (b) `` \,\mathrm{\,Half\,}-\,\mathrm{\,life\,},{T}_{1/2}=\frac{0.693}{\lambda }``
`` =2272.13\,\mathrm{\,s\,}``
`` =38\,\mathrm{\,min\,}``
Page No 443: (a) Activity, A = A0e-λt
Here, `` \lambda `` = Disintegration constant
`` \therefore `` 200 = 500 × e-50×60×λ
`` \Rightarrow \frac{2}{5}={e}^{-3000\lambda }``
`` \Rightarrow \,\mathrm{\,In\,}\frac{2}{5}=-3000\lambda ``
`` \Rightarrow \lambda =3.05\times {10}^{-4}{\,\mathrm{\,s\,}}^{-1}``
`` `` (b) `` \,\mathrm{\,Half\,}-\,\mathrm{\,life\,},{T}_{1/2}=\frac{0.693}{\lambda }``
`` =2272.13\,\mathrm{\,s\,}``
`` =38\,\mathrm{\,min\,}``
Page No 443:
- #23-aWhat is the decay constant of the sample?Ans : Activity, A = A0e-λt
Here, `` \lambda `` = Disintegration constant
`` \therefore `` 200 = 500 × e-50×60×λ
`` \Rightarrow \frac{2}{5}={e}^{-3000\lambda }``
`` \Rightarrow \,\mathrm{\,In\,}\frac{2}{5}=-3000\lambda ``
`` \Rightarrow \lambda =3.05\times {10}^{-4}{\,\mathrm{\,s\,}}^{-1}``
`` ``
- #23-bWhat is its half-life?Ans : `` \,\mathrm{\,Half\,}-\,\mathrm{\,life\,},{T}_{1/2}=\frac{0.693}{\lambda }``
`` =2272.13\,\mathrm{\,s\,}``
`` =38\,\mathrm{\,min\,}``
Page No 443: