The half life of cobalt -60 is 5.3 years. And if a half is 5.3 yrs long, then a period of 10.6 years have passed.
The activity of a radioactive sample is defined as the rate at which radioactive particles are emitted.
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 is 5.3 yrs long, then a period of 10.6 years have passed.
The half life equation is
A(t) = A0 (1/2) ^ t/t1/2
t1/2 = half life = 5.3 yes
A0 = intial quantity
A(t) = amount left after t years = 1/4 A0
t = time undergone =?
Substitute
1/4 A0 = A0 (1/2) ^ t/5.3
= 1/4 = (1/2) ^ t/5.3
Take the log of
log (1/4) = log { (1/2)^t/5.3}
= log)(1/4) = t/5.3 log (1/2)
Dividend both sides by log (1/2)
log (1/4) / log (1/2) = t/5.3 log(1/2) /log(1/4)
2 = t/5.3
t= 2.53 = 10.6 yrs
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