Final answer:
The average atomic mass of gold for a mixture of 50% gold-197 and 50% gold-198 is 197.5 amu. This is calculated using a weighted average based on the percentages and mass numbers of the isotopes.
Step-by-step explanation:
To calculate the average atomic mass of gold with two isotopes (gold-197 and gold-198), we will use a weighted average. A weighted average accounts for the percentage of each isotope present.
For gold-197: (0.50 × 197) = 98.5
For gold-198: (0.50 × 198) = 99
Add these values together to get the average atomic mass of gold: 98.5 + 99 = 197.5
Therefore, the average atomic mass of gold, given there are 50% gold-197 and 50% gold-198, is 197.5 atomic mass units (amu).