Rate of Radioactive Decay
Half Life Formula
The Half-Life series begins in the 2000s, at the fictional Black Mesa Research Facility in New Mexico. Gordon Freeman, a recently employed theoretical physicist, is involved in an experiment analyzing an unknown crystalline artifact; however, when the anti-mass spectrometer beam contacts the crystal, it creates a resonance cascade that opens a dimensional rift between Black Mesa and another.
- Half-Life 1 when released in November 1998 (just like Half-Life 2) was way ahead of it's time and included the Realistic Gameplay, Graphics, Narrative, and a lot more that explains why Half-Life 1 is one of the best games ever. This game is still One of the BEST games in 2020 or any other Game just like Half-Life 2.
- Half-Life: Directed by Randy Pitchford. With Kathy Levin, Lani Minella, Brice Armstrong, Harry S. Gordon Freeman must fight his way out of a secret research facility after a teleportation experiment goes disastrously wrong.
During natural radioactive decay, not all atoms of an element are instantaneously changed to atoms of another element. The decay process takes time and there is value in being able to express the rate at which a process occurs. A useful concept is half-life (symbol is (t_{1/2})), which is the time required for half of the starting material to change or decay. Half-lives can be calculated from measurements on the change in mass of a nuclide and the time it takes to occur. The only thing we know is that in the time of that substance's half-life, half of the original nuclei will disintegrate. Although chemical changes were sped up or slowed down by changing factors such as temperature, concentration, etc, these factors have no effect on half-life. Each radioactive isotope will have its own unique half-life that is independent of any of these factors.
The half-lives of many radioactive isotopes have been determined and they have been found to range from extremely long half-lives of 10 billion years to extremely short half-lives of fractions of a second. The table below illustrates half-lives for selected elements. In addition, the final elemental product is listed after the decal process. Knowing how an element decays (alpha, beta, gamma) can allow a person to appropriately shield their body from excess radiation.
| Element | Mass Number (A) | Half-life | Element | Mass Number (A) | Half Life |
|---|---|---|---|---|---|
| Uranium | 238 | 4.5 Billion years | Californium | 251 | 800 years |
| Neptunium | 240 | 1 hour | Nobelium | 254 | 3 seconds |
| Plutonium | 243 | 5 hours | Carbon | 14 | 5730 years |
| Americium | 245 | 25 minutes | Carbon | 16 | 740 milliseconds |
The quantity of radioactive nuclei at any given time will decrease to half as much in one half-life. For example, if there were (100 : text{g}) of (ce{Cf})-251 in a sample at some time, after 800 years, there would be (50 : text{g}) of (ce{Cf})-251 remaining. After another 800 years (1600 years total), there would only be (25 : text{g}) remaining.
Remember, the half-life is the time it takes for half of your sample, no matter how much you have, to remain. Each half-life will follow the same general pattern as (ce{Cf})-251. The only difference is the length of time it takes for half of a sample to decay.
Interactive Simulation: Visualizing Half-Life
Click on this interactive simulation to visualize what happens to a radioisotope when it decays. and learn about different types of radiometric dating, such as carbon dating. Understand how decay and half life work to enable radiometric dating. Play a game that tests your ability to match the percentage of the dating element that remains to the age of the object.
There are two types of half-life problems we will perform. One format involves calculating a mass amount of the original isotope. Using the equation below, we can determine how much of the original isotope remains after a certain interval of time.
[text{how much mass remains} = dfrac{1}{2^n} (text{original mass})]
(n) is the number of half-lives.
Example (PageIndex{1})
If there are 60 grams of (ce{Np})-240 present, how much (ce{Np})-240 will remain after 4 hours? ((ce{Np})-240 has a half-life of 1 hour)
Solution
[text{how much mass remains} = dfrac{1}{2^4} (60 , text{grams}) nonumber]
After 4 hours, only (3.75 : text{g}) of our original (60 : text{g}) sample would remain the radioactive isotope (ce{Np})-240.
Example (PageIndex{2})
A sample of (ce{Ac})-225 originally contained (8.0,ug). After 720 hours, how much of the original (ce{Ac})-225 remains? The half-life of this isotope is 10 days.
Solution
To determine the number of half-lives (n), both time units must be the same.
[720cancel{hours}times dfrac{1, day}{cancel{24 ,hours}}= 30, days nonumber]
[n=3 =dfrac{30 ,days}{10, days} nonumber]
Half-life Calculator
[text{how much mass remains} = dfrac{1}{2^3} (8.0 , ug) nonumber]
Half Life Of Caffeine
After 720 hours, 1.0 ug of the material remains as (ce{Ac})-225