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derive relationship between decay constant and half life.
Answers
Answer:
Decay constant, proportionality between the size of a population of radioactive atoms and the rate at which the population decreases because of radioactive decay. Suppose N is the size of a population of radioactive atoms at a given time t, and dN is the amount by which the population decreases in time dt; then the rate of change is given by the equation dN/dt = −λN, where λ is the decay constant. Integration of this equation yields N = N0e−λt, where N0 is the size of an initial population of radioactive atoms at time t = 0. 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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Answer:
Explanation:
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
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