What is the atomic mass of hafnium if, out of every 1000 atoms, 5 have a mass of 176 amu, 19 have a mass of 177 amu, 27 have a mass of 178 amu, 14 have a mass of 179 amu, and 35 have a mass of 180.0 amu?

*Note: there seems to be a "typo" in the given problem. The "1000" must probably be "100" only since summing up the total number of atoms given for the different isotopes would not equal 1000 but 100 instead. Using 1000 as the basis for the mass fractions would give an answer which is 10 times less than should be.

To determine the average atomic mass of halfnium, the mass fractions of the isotopes multiplied by their respected atomic masses must all be added. 

1. Determining the mass fractions (m1, m2...m5) with 100 atoms total as the basis: 

m1 =   5/100 = 0.05
m2 = 19/100 = 0.19
m3 = 27/100 = 0.27
m4 = 14/100 = 0.14
m5 = 35/100 = 0.35

2. Multiplying the mass fractions with the atomic masses of the respective isotopes. 

Average atomic mass of Halfnium
         = (m1*176) + (m2*177) + (m3*178) + (m4*179) + (m5*180) 
         = (0.05*176) + (0.19*177) + (0.27*178) + (0.14*179) + (0.35*180)
         = 178.55 amu

Thus, the average atomic mass of Halfnium based on the given data for its isotopes is 178.55 amu.