Derive the relation between half life and decay constant
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This shows that the population decays exponentially at a rate that depends on the decay constant. The time required for half of the original population of radioactive atoms to decay is called the half-life. The relationship between the half-life, T1/2, and the decay constant is given by T1/2 = 0.693/λ.
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Half life (T,T1/2,Th)
N=N°e^-lembda t
N°/2= N°e^-lembda T1/2
1/2= e^-lembdaT1/2
log base e (1/2)= log base e e^-lembdaT1/2
log base e (2^-1)=-lembda T1/2 log base e^e
-log e^2= -lembda T1/2
T1/2= 0.693/lembda
Where
Lembda is decay constant
T1/2 =half life period
N= remaining number of active nuclei
N°= initial number of active nuclei
✌️✌️
Answered by
5
Half life (T,T1/2,Th)
N=N°e^-lembda t
N°/2= N°e^-lembda T1/2
1/2= e^-lembdaT1/2
log base e (1/2)= log base e e^-lembdaT1/2
log base e (2^-1)=-lembda T1/2 log base e^e
-log e^2= -lembda T1/2
T1/2= 0.693/lembda
Where
Lembda is decay constant
T1/2 =half life period
N= remaining number of active nuclei
N°= initial number of active nuclei
✌️✌️
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