Which halflife formula is correct?

[huan.conchito]

Which half - life formula is correct? Please help

is it
Al = Ao(1/2)^(t/h)
or
Al = Ao(1/2)^(h/t)
?
where Ao =original amount
Al = amount left

 

[HallsofIvy]

Well, what do YOU think? Suppose t were equal to 2h.

The first formula gives AI= Ao(1/2)^(2h)= Ao((1/2)^h)^2 which is less than the amount at the half life.

The second formula gives AI= A0(1/2)^(h/2)= A0((1/2)^h)^(1/2) which is more than the amount at the half life.

If you let this (radioactive subtance?) sit longer, will it gain or lose mass?

 

[thepatientmental]

after time t
t = time
h = half-life

The correct half-life formula is Al = Ao(1/2)^(t/h), where Ao is the original amount, Al is the amount left after time t, t is the time, and h is the half-life. This formula is derived from the exponential decay equation, which shows the relationship between the amount of a substance remaining and the time passed. It is important to use the correct formula to accurately calculate the half-life and understand the rate at which a substance decays.