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Calculating the atomic mass of carbon using isotope data

The atomic mass of carbon can be calculated using the following information: Natural carbon is a mixture of three isotopes: 12^C, 13^C and 14^C. The carbon atoms are 98.59% of the isotope: 12^C, 1.11% of the isotope 13^C and <0.01% of the isotope 14^C. It has been decided that the atomic mass of the lightest carbon isotope should be exactly 12 u. Then the atomic masses of the two other isotopes will be 13.0034 u and 14.0032 u respectively.

To calculate the atomic mass of carbon, we need to determine the total mass of 10,000 atoms of natural carbon. To do this, we can use the following steps:

1. Calculate the mass of 10,000 atoms of the 12^C isotope: Since the 12^C isotope is the most abundant isotope in natural carbon, we can calculate its mass by multiplying the mass of a single atom of 12^C by the number of atoms present: (12 u) x (10,000 atoms) = 120,000 u.

2. Calculate the mass of 10,000 atoms of the 13^C isotope: We can do this in a similar way, by multiplying the mass of a single atom of 13^C by the number of atoms present: (13.0034 u) x (110 atoms) = 1433.374 u.

3. Calculate the total mass of 10,000 atoms of natural carbon: To do this, we can add the masses of the 12^C and 13^C isotopes: 120,000 u + 1433.374 u = 121,433.374 u.

4. Calculate the atomic mass of carbon: To find the atomic mass of carbon, we need to divide the total mass of 10,000 atoms of natural carbon by the number of atoms present: 121,433.374 u / 10,000 atoms = 12.1433374 u.


Therefore, the atomic mass of carbon is approximately 12.1433374 u. This value takes into account the fact that natural carbon is a mixture of different isotopes, with the 12^C isotope being the most abundant and the 14^C isotope being present in such a low concentration that it does not need to be taken into account.

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