How is the age of the cliffs determined?
Mountains and underground molten lava that cool down and turn into rocks are called igneous rocks. Uranium is also present in these rocks. Uranium is a radioactive element. Radioactive element elements automatically break down into another element's items over time. And by the same radioactivity, the age of nineteen rocks is calculated.
The uranium-235 radioactive in rock crystals is eventually broken down to lead-207. Now we have to find out the number of atoms of uranium-235 and lead-207 in one sample of the rock for which we have to determine the age. Uranium-235 and lead-207, are isotopes of uranium and lead.
This period is called the half-life of a radioactive element having half its number of atoms. The half-life of uranium-235 is some 700 million years.
If the number of lead-207 atoms in a rock sample is equal to the number of uranium-235 atoms, that rock is 700 million years old. Because of the number of uranium-235 atoms initially in this rock, half of them have converted to lead-207 after their first half-life.
50% of items are broken after the first half-life and 25% of the items are broken after the second half-life. That is, after two half-lives, 75% of uranium-235 atoms will be broken down to lead-207 and 25% will remain.
That is, if the number of lead-207 atoms in a rock sample is three times higher than that of uranium-235 atoms, it means that two lifetimes have passed and that rock is 1400 million years old.
It is no longer necessary that whatever rock sample we find contains the same number of uranium and lead atoms, or three times more than lead uranium. The number of these two items can be anything. So we need the help of a mathematical formula. The formula in the picture below gives the formula that we can solve for any number of atoms by removing the age of the rock. In this formula, NL represents the number of atoms of lead and NU, the number of uranium atoms. This number will be empirically extracted by analyzing the rock sample. The Lambda U in the formula is Decay Constant of uranium. The decay constants of all radioactive elements have been removed in practice. And t is the time we want to know. And if you've read Calculus, you know that e is the base of natural logarithm. Its aproximate value is 2.718.
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