# The units of unified atomic mass

There is something I don't understand about the units of unified atomic mass.

I have seen on Khan Academy that $$1$$ unified atomic mass ($$u$$) is equal to $$1.6605\times 10^{-27}$$ kg.

But after 2 videos he writes that the unit of $$u$$ is $$\frac{\mathrm{g}}{\mathrm{mol}}$$. Why is it true?
Why I can say that according to table of elements, for hydrogen, $$u=1.01 \frac{\mathrm{g}}{\mathrm{mol}}$$

• Suppose some eggs are 500 g/dozen. How much would they be per egg? – The Photon Oct 3 at 16:09

In SI units a mole is simply a number, a measure of quantity. It is defined as the number of atoms in $$12$$ grams of carbon $$12$$. Its value is approximately $$6.022 \times 10^{23}$$. So a mass of $$1$$ gram/mole in kg is
$$\displaystyle \frac {10^-3}{6.022 \times 10^{23}} \approx 1.66 \times 10^{-27}$$ kg
If an atom (or a molecule) has a mass of $$n$$ atomic mass units then one mole of that atom/molecule will have a mass of $$n$$ grams. One mole of carbon $$12$$ has a mass of exactly $$12$$ grams so one atom of carbon $$12$$ has a mass of exactly $$12$$ atomic mass units.
The reason that one atom of hydrogen has a mass slightly greater than $$1$$ atomic mass unit is because an atom of carbon $$12$$ is slightly less than $$12$$ times as massive as an atom of hydrogen, due to binding energy.