The standard atom for the atomic masses of all the elements is the atom of carbon which has 6 protons and 6 neutrons (12C) and is assigned the atomic mass of exactly 12. Under this standard, the atomic mass of iron, atomic number 26, is 55.845 u and the atomic mass of gold, atomic number 79, is 196.967 u. If, however, the atom of gold which contains 79 protons and 118 neutrons (197Au) were to be made the standard instead of the atom of 12C, and assigned the atomic mass of exactly 200, what would the atomic mass of iron become?

How would you solve this? Would you set a ratio between Au-197 and the relative atomic mass of Fe or a ration between the relative atomic mass of Au and Fe? If it's the latter why?

The ratio of Fe to Au, based on C-12=12.00 is 55.845/196.957 = 0.2835390

and that number x 200 = ?? mass Fe based on Au at 200 instead of 196.957. I have used more significant figures in the ratio above than is justified but you can pare that down with the final answer. Another way to look at it is just as you would do a dimensional analysis problem.
Fe(@C=12.00) x (Au@200/Au@C=12.00)=
55.845 x (200/196.957) = ?? Fe @ Au=200
Check my thinking. Check my arithmetic.

the answer is 60

To solve this problem, we need to determine the atomic mass of iron (Fe) in the new standard, where the atom of gold (Au) is assigned the atomic mass of exactly 200.

It might initially seem logical to set a ratio between Au-197 and the relative atomic mass of Fe, but this approach would not be correct in this case. The reason is that the ratio of atomic masses between different elements cannot be determined by the ratio of their individual isotopes alone.

Instead, we need to use the concept of relative atomic mass. The relative atomic mass of an element is the weighted average of the masses of all naturally occurring isotopes of that element, taking into account their abundances.

Since we are considering a new standard atom (Au-197 in this case), we need to determine the relative atomic mass of that isotope. The atomic mass of Au-197 is approximately 197 u, but keep in mind that this might not be the exact value.

Now, let's calculate the atomic mass of iron (Fe) in this new standard. We can set up the following equation using the concept of relative atomic mass:

(atomic mass of Fe) / (atomic mass of Au-197) = (relative atomic mass of Fe) / (relative atomic mass of Au-197)

Using the given values of atomic masses, we can plug them into the equation:

(atomic mass of Fe) / 197 = (relative atomic mass of Fe) / 200

We can now rearrange the equation to solve for the atomic mass of iron:

atomic mass of Fe = (relative atomic mass of Fe / 200) * 197

To find the atomic mass of iron in the new standard, we need the relative atomic mass of iron in that standard, which is not given in the question. Without that information, we cannot determine the exact value of the atomic mass of iron in the new standard.