# Suppose the amu had been defined as #1/10#th of the mass of a phosphorus atom. What would be the relative mass of carbon-12?

##### 1 Answer

#### Explanation:

So, let's say that you pick a phosphorus atom, more specifically a *phosphorus-31* atom, since that is the only stable isotope of phosphorus, as the base for the *unified atomic mass unit*, or

The main idea here is that the **relative atomic masses** of two atoms *do not change* when the unified atomic mass unit changes because the atoms themselves do not change as a result of that.

This means that you can use the *current* definition of **must exist** between a phosphorus-31 atom and a carbon-12 atom for different values of

So, the current definition of

#"1 u = 1 g/mol"#

you can use the current atomic masses of phosphorus-31 and carbon-12 to find the ratio that must exist between these two atoms

#A_"r phosphorus-31"/A_"r carbon-12" = "30.9738 u"/"12.011 u" = (30.9738 color(red)(cancel(color(black)("g/mol"))))/(12.011color(red)(cancel(color(black)("g/mol")))) = 2.578786 " " "color(blue)((1))#

This means that a phosphorus-31 atom is **heavier** than a carbon-12 atom.

The atomic mass of **a mole** of phosphorus-31 atoms is known to be **one atom** of

#30.9738"g"/color(red)(cancel(color(black)("mole"))) * (1color(red)(cancel(color(black)("mole"))))/(6.022 * 10^(23)"atoms of P") = 5.1434 * 10^(-23)"g/atom"#

Now, you need

#"1 u" = (5.1434 * 10^(-23)"g")/10 = 5.1434 * 10^(-24)"g"#

If *one mole* of phosphorus using the new definition of

#A_"r phosphorus-31" = 1/10 * "30.9738 u" = "3.09738 u"#

This means that the relative atomic mass of carbon-12 will be, using equation

#A_"r carbon-12" = "3.09738 u"/2.578786 = color(green)("1.2011 u")#