To calculate the atomic mass of gallium in this hypothetical universe, we use the formula for the weighted average atomic mass, which accounts for the abundance and mass of each isotope.

The formula is:

$\text{Atomic mass of Ga} = \left( \frac{\% \text{abundance of } 71\text{Ga}}{100} \times \text{mass of } 71\text{Ga} \right) + \left( \frac{\% \text{abundance of } 69\text{Ga}}{100} \times \text{mass of } 69\text{Ga} \right)$

Given:

• The abundance of $71 \text{Ga} = 61.483\%$
• The mass of $71 \text{Ga} = 70.9247 \, \text{au}$
• The abundance of $69 \text{Ga} = 100\% - 61.483\% = 38.517\%$
• The mass of $69 \text{Ga} = 68.9256 \, \text{au}$

Substituting the values into the formula:

$\text{Atomic mass of Ga} = \left( \frac{61.483}{100} \times 70.9247 \right) + \left( \frac{38.517}{100} \times 68.9256 \right)$

Let's calculate this now.The atomic mass of gallium in this hypothetical universe is approximately $70.155 \, \text{au}$, rounded to three decimal places.

Would you like more details or have any questions about the process? Here are some related questions to explore:

1. How is atomic mass determined in real-world experiments?
2. What are isotopes, and how do they affect atomic mass?
3. How does the abundance of isotopes vary across different elements?
4. Can the atomic mass of an element change over time?
5. How do isotopic masses influence chemical reactions?

Tip: Always keep track of units during calculations to ensure consistency and accuracy.