What is Carbon dating? Formula to calculate Carbon dating

 What is Carbon Dating?

Carbon dating, also called radiocarbon dating, is a technique used to date materials that once traded carbon dioxide with the climate. At the end of the day, things that were living. In the late 1940s, an American physical scientist named Willard Libby originally built up a technique to gauge radioactivity of carbon-14, a radioactive isotope. Libby was granted the Nobel Prize in science for his work in 1960.

Carbon dioxide in the climate contains a steady measure of carbon-14, and up to a living being is living, the measure of carbon-14 inside it is equivalent to the environment. Be that as it may, when the living being bites the dust, the measure of carbon-14 consistently diminishes. By estimating the measure of carbon-14 remaining in the life form, it's conceivable to turn out how old it is. This method functions admirably for materials up to around 50,000 years of age.

Carbon/Radioactive Half-Lives

Each radioactive isotope rots by a fixed sum, and this sum is known as the half-life. The half-life is the time required for half of the first example of radioactive cores to rot. For instance, on the off chance that you start off with 1000 radioactive cores with a half-existence of 10 days, you would have 500 remaining following 10 days; you would have 250 remaining following 20 days (2 half-lives, etc. The half-life is consistently the equivalent paying little mind to what number of cores you have left, and this valuable property lies at the core of radiocarbon dating.

Carbon-14 has a half-existence of around 5,730 years. The chart beneath shows the rot bend (you may remember it as an exponential rot) and it shows the sum, or percent, of carbon-14 remaining. You will see that after around 40,000 years (or 8 half-lives), the sum left is beginning to turn out to be exceptionally little, under 1%. Researchers frequently utilize the estimation of 10 half-lives to show when a radioactive isotope will be gone, or rather, when an entirely unimportant sum is still left. This is the reason radiocarbon dating is just valuable for dating objects up to around 50,000 years of age (around 10 half-lives).

Formula to discover carbon dating

Radioactive isotopes, such as ¹⁴C, decay exponentially. The half-life of an isotope is defined as the amount of time it takes for there to be half the initial amount of the radioactive isotope present.

For example, suppose you have N₀ grams of a radioactive isotope that has a half-life of t* years. Then we know that after one half-life (or t* years later), you will have

½ *N₀ =N₀/2  grams of that isotope.

t* years after that (i.e. 2t* years from the initial measurement), there will be

½* ½*N₀ =(½)² *N₀ =N₀/4 grams.

3t* years after the initial measurement there will be

½*½*½*N₀ =(½)³ * N₀ =N₀/8  grams

and so on.

We can use our our general model for exponential decay to calculate the amount of carbon at any given time using the equation,

	N (t)=N0 ekt

 

 

Modeling decay of  ¹⁴C

Returning to our example of carbon, knowing that the half-life of ¹⁴C is 5700 years, we can use this to find the constant, k. That is when t = 5700, there is half the initial amount of ¹⁴C. Of course the initial amount of ¹⁴C is the amount of ¹⁴C when t = 0, or N₀ (i.e. N(0) = N₀e ^k⋅0 = N₀e⁰ = N₀). Thus, we can write

  N(5700)=N₀/2 =N₀ ^k*5700

Simplifying this expression by canceling the N₀ on both sides of the equation gives,
½=e^5700k

for the unknown, k, we take the natural logarithm of both sides,

Solving ln(1/2)=ln e^5700k

             k=ln(1/2)     ≈ -0.0001216

 5700

finally, our equation for modeling the decay of ¹⁴C becomes,

N(t) ≈N₀e^-0.0001216t