It's a process involving experimentation and mathematical modelling.
Method #1:
One way to solve for half-life is to use the following equation:
t1/2 = (t ln 1/2)/(ln mf/mi)
where:
t1/2 = half-life
t = time that has passed
mf = the final or remaining mass of undecayed sample
mi = the initial or original mass of undecayed sample
(The fraction mf / mi is of course equivalent to the fraction or percentage of undecayed sample remaining, in case you are given the fraction remaining rather than specific masses.)
Note: You can also use base-10 logarithms instead of natural logarithms.
For instance, you are told that after 2.00 hours a sample decays such that 80.0% remains undecayed. Substituting these values into the formula allows us to find the half-life of the substance in essentially one step:
t1/2 = (2.00*ln(0.5))/(ln(0.800)) = 6.21 hours
Method #2:
Half-life can alternatively be found in a two-step process using the related model:
At = A0e-Bt
where:
At = Amount at time t
A0 = Initial amount
e = exponential
B = a constant
t = time
However, before you can determine a half-life, first you need to determine what the constant, B, is. This can be done via experimentation. For example, imagine you are observing the decay of a radioactive substance. After 2.00 hours you determine that you only have 80.0% left of the initial amount...
That is, A2 = 0.800A0
So, 0.800A0 = A0e-2.00B
Rearrange to get B = -ln(0.800)/2.00 = 0.1116
So now you have what you need to determine the half life. That is, how many hours will it take before you only have 50.0% left of the decaying substance?
As above, 0.500A0 = A0e-Bt
Solving for t this time, t = -ln(0.5)/B = -ln(0.5)/0.1116 = 6.21 hours.
Note: As in the other method, you could also have used base-10 logarithms instead of base-e (natural) logarithms. Just be sure to use the same base in all your calculations.
As you can see, both these methods yield the same answer, a half-life for the substance of 6.21 hours.
Another Answer:
First you have to find the rate of decay for whatever "half-life" problem you're trying to solve. Try this formula to find the half-life:
-ln(2)=tk
Where t stands for years and k stands for the rate of decay. You'll always be given one of these, just plug in either the years to find the rate of decay or plug in the rate to find the # of years.
Another Answer:
In order to solve half-life equations, consider the equation ...
AT = A0 2(-T/H)
... where A0 is the initial radioisotope's activity, AT is the decayed activity after time T, and H is the half-life. Given 3 of these parameters, you can solve for the fourth. For instance, given starting activity, ending activity, and time, you can solve for half-life as follows ...
AT = A0 2(-T/H)
AT/A0 = 2(-T/H)
ln2(AT/A0) = -T/H
H = -T/ln2(AT/A0)
... and don't forget that ln2(x) = log(x)/log(2)
c.half-life
Promethium 145 has a half life of 17.7 years. Promethium 146 has a half life of 5.53 years. Promethium 147 has a half life of o.22 years.
The length of time for the second half-life is the same as the first half-life. Each half-life represents the time it takes for half of the radioactive atoms in a sample to decay. This process continues exponentially with each subsequent half-life.
Half-life is described in time units.
Planet Half-Life was created in 1999.
No. Half Life: Opposing Force does not require neither Half Life nor Half Life: Blue Shift.
You will never succeed in life if you can't solve problems yourself!
The half-life is the time it takes for half of the sample to decay. The formula to use is N(t) = N(0) / 2^(t/half life), where N(0) is what we have at the start, and N(t) what is left at time t.
No, only Half-Life and Half-Life: Decay.
The time it takes for half the atoms in a sample of a radioactive element to decay is called the half life.
Antibiotics do not have a half life.
You say 'I've missed Half my life' which is short for : "I have missed half my life'
The term is called half-life. It is the time it takes for half of the radioactive nuclei in a sample to decay.
Buy Half Life: Source Or Buy Garrysmod a Half-Life 2 Modification and get the addon "Half-Life Rennaisance" Link to Half Life Rennaisance: http://www.garrysmod.org/downloads/?a=view&id=57033 Enjoy!
No. Half-Life: Source runs on the Source engine. The original Half-Life doesn't. You cannot use mods made for the original Half-Life on Half-Life: Source because they run on different engines and it won't work.
No
There is no "Half Life 3" If you're talking about Half-Life 2, then no, but you can get Counter-Strike.