In another universe, gallium has two major isotopes, 71Ga and 69Ga, just like in our universe.  But the abundance of each isotope is different.  

71Ga has a mass of 70.9247 au and an abundance of 61.483%

69Ga has a mass of 68.9256 au and an abundance of (100 - 61.483)%

What is the atomic mass of Ga in the other universe?  Give your answer to 3 places behind the decimal.



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.

In another universe, gallium has two major isotopes, 71Ga and 69Ga, just like in our universe. But the abundance of each isotope is different. 71Ga has a mass of 70.9247 au and an abundance of 61.483%, 69Ga has a mass of 68.9256 au and an abundance of (100 - 61.483)%. What is the atomic mass of Ga in the other universe? Give your answer to 3 places behind the decimal.

Learn how to calculate the atomic mass of gallium in a hypothetical universe by using the weighted average formula. This problem involves isotopic abundances of 71Ga and 69Ga, with a mass of 70.9247 au and 68.9256 au respectively, and teaches how to apply percentages in atomic mass calculations. Suitable for students in Grades 10-12.

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