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
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
The atomic mass of a mole of phosphorus-31 atoms is known to be
#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
#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")#