Please examine the following scenario.
I am a famous paleontologist and an expert in radioactive-dating techniques. One day, two visitors to my laboratory present me with two different fossils. One fossil is a dinosaur footprint, the other a human jawbone. Both were found at the bottom of a deep valley cut by a stream through cliffs of sedimentary rock. My guests are very excited. Because the visitors have found these fossils next to each other near the stream bed, they feel they have found conclusive evidence that humans and dinosaurs lived at the same time. I am asked to date the samples to confirm their claims.
I first test the human jawbone. I determine that it now contains 1/16 the amount of carbon-14 it contained when it was alive. How old is the jawbone?
I next examine the fossil footprint. I discover that the fresh mud the dinosaur stepped in had just been covered with a thin layer of volcanic ash. I study the amount of potassium-40 and argon-40 in the ash. The ratio shows that 1/10 of one potassium-40 half-life has passed since the footprint was made. How old is the footprint?
Sample chart of half-lives of radioactive elements:
Potassium-40 1.3 billion years (half-life)
Carbon-14 5770 years
Were my visitors' conclusions about these fossils' ages correct? If they were not, how could I explain the fact that they were found together at the bottom of the valley?
Because the two objects were found at the site site does not mean they lived at the same time. We already know, through carbon dating, the dinosaur footprint is much older than the human jawbone. Landscapes change over time and things get moved around, especially when this many years are in question.
If you have worked through the information in the links posted by ask996, you already know they are not the same age. As to how they came to be in the same place, the bottom of a stream-cut valley through sedimentary rock has had its many layers eroded over a very long time. These two artifacts were no doubt dislodged from their respective layers, and ended up near each other by the action of the stream and gravity.
You’ve provided us with such explicit information and such specific questions, that I think this should probably be posted on the question discussion board. Be that as it may, e-notes has some links on both radiocarbon dating and radiometric dating. Those might give you more information.
Based on the information given the Jawbone is about 23000 years old. We get this figure by multiplying half life of carbon-14 by 4. The foot print is 130,000 years old, which is one tenth the half life of potassium-40.
Both these objects cab be found at the same place in spite of difference of their age. As a matter of fact, if your friend had by mistake made some finger prints at the same site, the next day he could have found his one day old finger prints also there.