If you are curious whether or not there is carbon 14 in dinosaur bones, the answer is yes. But what does that mean?
Or, you can read on for a brief discussion about the math behind the procedure; don’t worry, it’s not very difficult. I’ll make it simple here.
Scientists know the decay-rate of carbon-14 atoms. They can measure this by observation in the laboratory — this is called “empirical science,” or the process of acquiring knowledge through experimentation. In the following equation, this decay-rate value that they measure is “r”:
“r” is called the decay constant. “t” is a period of time. “Y[init]0” is the initial amount of the carbon-14 present. “Y” is the final amount of the carbon-14 present after a period of time, “t.”
WHAT WE CAN LEARN BASED ON WHAT WE CAN MEASURE
So, according to this equation (which allows us to calculate the exponential rate of change and is technically the solution to a differential equation), assuming we know “r” (which modern science does), you can solve for different unknowns depending on what information you have at your fingertips:
- Determine “Y”, the amount of an element that will be remaining after time “t” if you know how much “Y0” you are starting with.
- Determine “Y0“, the amount of an element that was present initially, in the past, if you can measure how much “Y” you have today and you know how much time has passed since the initial amount was deposited.
- Determine how much time, “t”, has passed if you know how much “Y” is present today and how much “Y0” was present in the beginning.
Let’s quickly discuss another concept: decay constants. The value “1/r” is generally referred to as one time constant. Since “r” for carbon-14 is equal to -0.000121, “1/r” is equal to approximately 8,264 years.
After about 7 time constants, most of the element will have decayed. 7 x 8,264 is equal to 57,848 years.
While scientists speak in time constants, a generally helpful idea for most people is the “half life,” or the amount of time it takes for approximately half of an element to decay. Assuming an initial amount of 2, and a final amount of 1 (half the initial amount), and exponentiating both sides of the equation, you come up with the following solution for “t”:
t = ln(1/2) ÷ r = -0.693 ÷ -0.000121 = 5,728 years
Accordingly, it takes about 10 half-lives for most of the initial amount to decay: 57,280 years.
So, in short, after about 60,000 years, there would be no measurable carbon-14 left remaining in any given sample — it will have all decayed.
JUST FOR A MOMENT, ASSUME YOU DON’T KNOW HOW OLD DINOSAURS ARE
If dinosaur bones contain enough carbon-14 that we can measure the amounts, and you pretended not to “know” that dinosaur bones were 60 million years old, how old would you think they were?
Less than 60,000 years, right? That makes sense, right? You wouldn’t be able to determine much more than that since, according to scenario #3 above, you weren’t actually around to measure how much carbon-14 was present in the dinosaur’s bones when it first died. But you could generally state that the bones are less than 60,000 years old intelligently — based on information you can measure.
If you want to guess how much carbon-14 was present in the beginning, then you can come up with different conclusions.
The problem is that scientists guess and make an assumption: dinosaurs died 60 million years ago. Therefore, when they look at this data, they have a very hard time explaining the presence of carbon-14.
In fact, they normally don’t bother measuring dinosaur bones because they assume there is no carbon-14 in them.
But some scientists have measured dinosaur bones, and they did find carbon-14 in them.