Nuclear HalfLife Calculations
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Key Questions

Answer:
Halflife is the time it takes for half the population of a sample to change into something else.
See BelowExplanation:
It is mostly used for radioactive decay. So when an isotope is unstable in it's nucleus (because of too many neutrons, for example), the atom will undergo a process that alters the nucleus (number of protons and electrons).
Radioactive Carbon is an example, C14. It has 6 protons and 8 neutrons. Its nucleus is unstable because of the ratio of neutrons to protons. In order to become more stable, one of the neutrons (we are going to say a neutron is composed of a proton+electron....this is what our simplistic neutron is) is going to break apart. The electron that is bound in the neutron comes 'flying out', and this is called a beta particle.
The C14 atom has just undergone radioactive decay. Now the atom has only 7 neutrons...and 1 extra proton (that it got from the breaking apart neutron). So now the Carbon atom is actually a Nitrogen atom with 7 protons and 7 neutrons.....and it is stable. This is radioactive decay.
It is very hard to determine when 5 atoms change, 10 atoms change...but it is easier to see when half the population changes.
If you have a sample of Carbon14, it will undergo this radioactive decay, and the time it takes for HALF of the Carbon14 atoms to change into Nitrogen is called the Half Life of Carbon14.So, radioactive elements have half lives. It is the time it takes for half of them to decay into a new element.
As an aside, halflife is also sometimes used when talking about things like drugs. If you take Drug X, it will be in your blood, for example..and will slowly (or quickly) start to fall apart in the body. THe time it takes for half the drug to change into something else (usually modified by the body or labile bonds get hydrolized), is the drugs halflife. In this case, it is not radioactive, but rather just falling apart inside the body.

Nuclear halflife expresses the time required for half of a sample to undergo radioactive decay. Exponential decay can be expressed mathematically like this:
#A(t) = A_0 * (1/2)^(t/t_("1/2"))# (1), where#A(t)#  the amount left after t years;
#A_0#  the initial quantity of the substance that will undergo decay;
#t_("1/2")#  the halflife of the decaying quantity.So, if a problem asks you to calculate an element's halflife, it must provide information about the initial mass, the quantity left after radioactive decay, and the time it took that sample to reach its postdecay value.
Let's say you have a radioactive isotope that undergoes radioactive decay. It started from a mass of 67.0 g and it took 98 years for it to reach 0.01 g. Here's how you would determine its halflife:
Starting from (1), we know that
#0.01 = 67.0 * (1/2)^(98.0/t_("1/2")) > 0.01/67.0 = 0.000149 = (1/2)^(98.0/(t_("1/2"))# #98.0/t_("1/2") = log_(0.5)(0.000149) = 12.7# Therefore, its halflife is
#t_("1/2") = 98.0/(12.7) = 7.72# #"years"# .So, the initial mass gets halved every 7.72 years.
Sometimes, if the numbers allow it, you can work backwards to determine an element's halflife. Let's say you started with 100 g and ended up with 25 g after 1,000 years.
In this case, since 25 represents 1/4th of 100, two hallife cycles must have passed in 1,000 years, since
#100.0/2 = 50.0# #"g"# after the first#t_("1/2")# ,#50.0/2 = 25.0# #"g"# after another#t_("1/2")# .So,
# 2 * t_("1/2") = 1000 > t_("1/2") = 1000/2 = 500# #"years"# . 
Answer:
T=th xlog(m./m)/log(2)
Explanation:
You could use this formula:
Where Th = halflife.
M. = the beginning amount
M = the ending amountOne example of how to use the equation:
One of the Nuclides in spent nuclear fuel is U234, an alpha emitter with a halflife of 2.44 x10^5 years. If a spent fuel assembly contains 5.60 kg of U234, how long would it take for the amount of U234 to decay to 0.35? First, break down the complicated equation:
T= unknown
Th= 2.44 x10^5 or 244000
M.= 5.60
m= 0.35Then plug the number into the equation:
T= 244000 xlog(5.60/0.35)/log(2)
T= 244000x1.20412/log(2)
So the Answer is: T= 9.76x10^5 min.
Note: The example was a question from my quiz I took three weeks ago!
Questions
Nuclear Chemistry

1Nuclear Chemistry

2Isotope Notation

3Isotope Stability

4Alpha Decay

5Beta Decay

6Positron Decay

7Electron Capture

8Nuclear Equations

9Nuclear HalfLife

10Nuclear HalfLife Calculations

11Nuclear Transmutation

12Fission and Fusion

13Applications of Nuclear Chemistry

14Biological Effects of Radiation