Question #1f8ff

1 Answer
Nam D.
Jan 12, 2018

We can use a radioactive decay equation.

Explanation:

Radioactive decay is a random process, so we cannot exactly know which atom or the order that the atoms are going to decay. But, a formula can work to find the general half-life of a substance.

It is given by

#N(t)=N_0(1/2)^(t/(t_1/2))#

#N(t)# is the final amount of substance

#N_0# is the original amount of the substance

#t# is the time

#t_(1/2)# is the half-life of the substance

So, we can derive the half-life of the substance by rearranging the equation. Our original equation is

#N(t)=N_0(1/2)^(t/(t_1/2))#

Dividing by #N_0# gives us

#(N(t))/N_0=(1/2)^(t/(t_1/2))#

Using the logarithm properties, we get that

#t/(t_(1/2))=log_(1/2)((N(t))/N_0)#, and then we can inverse and get the reciprocal, which is

#(t_(1/2))/t=1/log_(1/2)((N(t))/N_0)#

Solving for #t_(1/2)#, we get

#t_(1/2)=t/log_(1/2)((N(t))/N_0)#

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