NEET-XII-Physics
46: The Nucleus
- #29-aIs it a β+-decay or a β-decay? (b) The half-life of the decay scheme is 20.3 minutes. How much time will elapse before a mixture of 90% carbon-11 and 10% boron-11 (by the number of atoms) converts itself into a mixture of 10% carbon-11 and 90% boron-11? (b) The half-life of the decay scheme is 20.3 minutes. How much time will elapse before a mixture of 90% carbon-11 and 10% boron-11 (by the number of atoms) converts itself into a mixture of 10% carbon-11 and 90% boron-11?Ans : The reaction is given by
`` {\,\mathrm{\,C\,}}_{6}\to {\,\mathrm{\,B\,}}_{5}+{\,\mathrm{\,\beta \,}}^{+}+\,\mathrm{\,v\,}``
It is a β+ decay since atomic number is reduced by 1. (b) Half-life of the decay scheme, T 1/2 = 20.3 minutes
Disintegration constant, `` \lambda =\frac{0.693}{{T}_{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}}`` = `` \frac{0.693}{20.3}{\,\mathrm{\,min\,}}^{-1}``
If t is the time taken by the mixture in converting, let the total no. of atoms be 100N0.
Carbon Boron Initial 90 N0 10 N0 Final 10 N0 90 N0
N = N0e-λt
Here, N0 = Initial number of atoms
N = Number of atoms left undecayed
10N0 = 90N0e-λt ( For carbon)
`` \Rightarrow \frac{1}{9}={e}^{-\frac{0.693}{20.3}\times t}``
`` \Rightarrow \,\mathrm{\,In\,}\frac{1}{9}=\frac{-0.693}{20.3}t``
`` \Rightarrow t=64.36=64\,\mathrm{\,min\,}``
Page No 443: (b) Half-life of the decay scheme, T 1/2 = 20.3 minutes
Disintegration constant, `` \lambda =\frac{0.693}{{T}_{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}}`` = `` \frac{0.693}{20.3}{\,\mathrm{\,min\,}}^{-1}``
If t is the time taken by the mixture in converting, let the total no. of atoms be 100N0.
Carbon Boron Initial 90 N0 10 N0 Final 10 N0 90 N0
N = N0e-λt
Here, N0 = Initial number of atoms
N = Number of atoms left undecayed
10N0 = 90N0e-λt ( For carbon)
`` \Rightarrow \frac{1}{9}={e}^{-\frac{0.693}{20.3}\times t}``
`` \Rightarrow \,\mathrm{\,In\,}\frac{1}{9}=\frac{-0.693}{20.3}t``
`` \Rightarrow t=64.36=64\,\mathrm{\,min\,}``
Page No 443:
- #29-bThe half-life of the decay scheme is 20.3 minutes. How much time will elapse before a mixture of 90% carbon-11 and 10% boron-11 (by the number of atoms) converts itself into a mixture of 10% carbon-11 and 90% boron-11?Ans : Half-life of the decay scheme, T 1/2 = 20.3 minutes
Disintegration constant, `` \lambda =\frac{0.693}{{T}_{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}}`` = `` \frac{0.693}{20.3}{\,\mathrm{\,min\,}}^{-1}``
If t is the time taken by the mixture in converting, let the total no. of atoms be 100N0.
Carbon Boron Initial 90 N0 10 N0 Final 10 N0 90 N0
N = N0e-λt
Here, N0 = Initial number of atoms
N = Number of atoms left undecayed
10N0 = 90N0e-λt ( For carbon)
`` \Rightarrow \frac{1}{9}={e}^{-\frac{0.693}{20.3}\times t}``
`` \Rightarrow \,\mathrm{\,In\,}\frac{1}{9}=\frac{-0.693}{20.3}t``
`` \Rightarrow t=64.36=64\,\mathrm{\,min\,}``
Page No 443: