Respuesta :
The relationship between decay constant and half-life is [tex]k= \frac{1n2}{t_{1/2} }[/tex]
the half life of ⁹⁰Kr = 32s
calculate the decay constant as follows:
[tex]k= \frac{1n2}{t_{1/2} }[/tex]
[tex]= \frac{1n2}{32s }[/tex]
[tex]= 0.0216608s^{-1}[/tex]
Therefore the decay constant is [tex]0.0216608s^{-1}[/tex]
What is decay constant?
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.
Learn more about decay
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