My textbook explains that the deviation from integer atomic mass is caused by mass difference between proton and neutron, which are $1.67262·10^{-27}$ kg and $1.67493 ·10^{-27}$ kg, respectively.
If SI system currently define $1$ mole as the number of entities in exactly $12$ g of $C^{12}$, which is Avogadro's number $N_A = 6.02214\times 10^{23}$, then $$6.02214\times10^{23} ( C^{12}) = 12g$$ Likewise atomic mass unit (u) for relative mass is also defined by $C^{12}$ isotope as $12 u = C^{12}$ atom. So $$1 g = 6.02214\times 10^{23}u$$ Then if $12 u = 6(m_{proton}+m_{neutron}+m_{electron})=1C^{12}$, and $m_{proton}<m_{neutron}$ (as stated by the text), $$6\times\frac{m_{proton}}{m_{total}}<\frac1{2}$$proton mass ratio in carbon-$12$ is less than half, and one proton mass will be $m_{proton}$ $1 u$ = $1.66054 ·10^{-27}$ kg
This proton mass is less than the value in the book $1.67262·10^{-27}$ kg and would produce a much lower atomic mass for $H^1$ than $1.00783$ u. Catastrophic! Why is this and what am I missing here?
