# What is the relation between the amu and avogadro’s number? [closed]

I know that the relation between Avogadro’s number and amu is a reciprocal relationship but the relation is slightly unclear.

Could anyone give me more clarification?

• $$N_{A} = \frac{m_{\mathrm{in\ amu}}}{m_{\mathrm{in\ grams}}}$$ – Zhe Mar 9 '17 at 23:15

$\pu{1amu}$ is defined as one twelfth of the mass of one carbon-12 atom.

Avogadro's number is defined as the total number of entities in $\pu{12g}$ of carbon-12.

$N_\mathrm A=6.022\times10^{23}$

It is a measuring criteria, just like a dozen, which is used to put a number to a certain item. A dozen means 12 items (items like bananas, atoms, molecules, etc) and 1 mole means $6.022\times10^{23}$ items (items like bananas, atoms, molecules, etc).

So, $\pu{12g}\ \ce{^12C}$ contains $N_\mathrm A$ atoms

Therefore, 1 atom of carbon-12 weighs $\frac{12}{N_\mathrm A}\ \mathrm{g}$.

As per the defintion of atomic mass unit, $$\pu{1amu}=\frac{1}{12}\frac{12}{N_\mathrm A}\mathrm{\ g}=\frac{1}{6.022\times10^{23}}\ \mathrm{g}$$

Hence, $\pu{1amu}=\pu{1.6\times10^{-27}kg}$

• I don’t know where your obscure unit gram-metres derive from, but I’m reasonably sure you were trying to talk about grams all across this answer so I corrected that. – Jan Oct 8 '17 at 15:00
• It wasn't meant to be interpreted as $gram-meter$, I used to the notation 'gm' for gram. However, thanks for the edit. – Mitchell Oct 8 '17 at 17:37
• If you wanted to write grams, please use the standard SI-conform abbreviation $\mathrm g$ and not any made-up non-standard ones. Everything else will cause confusion. – Jan Oct 8 '17 at 17:46
• Yeah, I got that. – Mitchell Oct 8 '17 at 17:47

The atomic mass unit (amu or simply u) is the $1/12$ of the mass of a $\ce{^12C}$ atom.
Avogadro's number ($N_\mathrm A=6.022\times10^{23}$) is the number of atoms contained in $\pu{12g}$ of $\ce{^12C}$.

The relation between them has to do with relative atomic mass ($A_\mathrm r$), which is basically the number of atomic mass units an atom is equal to. One can easily understand that carbon is equal to $\pu{12u}$, hydrogen to $\pu{1u}$, helium to $\pu{4u}$, etc. (I'm referring to the most common isotopes)

Now, $N_\mathrm A$ atoms (or $\pu{1 mol}$) weigh $A_\mathrm r\ \mathrm{g}$. For example, $N_\mathrm A$ atoms of hydrogen weigh $\pu{1g}$. This is because they are the $1/12$ of $N_\mathrm A$ atoms of carbon (which weigh $\pu{12g}$).