The half-life of cobalt-60 is 5.3 years. How many years will it take for 1/4 of the original amount of coblat-60 to remain?

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Answer 1 · 2017-10-22T09:26:08

It this not TWO half-lives.....?

After one-life, #1/2# the mass of the original isotope remains. After another half-life, #1/4# the mass of the original isotope remains.

And if a half-life is #5.3# years long, then this is a period of 10.6 years.....

How long until #1/16# of the original mass remains?

Answer 2 · 2017-10-22T09:36:28

#10.6yrs#

The half-life equation is :

#A(t)=A_0*(1/2)^(t/(t_("1/2"))#

What we know:

#t_("1/2")->"half-life"=5.3yrs.#

#A_0->"Initial quantity"#

#A(t)->"Amount left after t years"=1/4 A_0#

#t->"time undergone"=color(blue)(?#

Substituting in the equation:

#=1/4cancel(A_0)=cancel(A_0)*(1/2)^(color(blue)t/5.3)#

#=1/4=(1/2)^(color(blue)t/5.3)#

Take the #log# of both sides:

#log(1/4)=log((1/2)^(color(blue)t/5.3))#

#=log(1/4)=color(blue)t/5.3*log(1/2)#

Dividend both sides by #color(red)(log(1/2)#

#=cancel(log(1/4)/color(red)(log(1/2)))^2=color(blue)t/5.3*cancel(log(1/2)/color(red)(log(1/2))#

#=2=color(blue)t/5.3#

#=>color(blue)t=2*5.3=10.6yrs.#