Question

Suppose that hypothetical element Jovian occurs as three isotopes with mass numbers 44, 46, and 48 respectively. If, in nature, Jovian occurs as Jovian-44 approximately 22.4% of the time, and as Jovian-46 approximately 44.0% of the time, what is the best value to use as the atomic mass of Jovian?(1 point)
Responses

46.2 amu
46.2 amu

46.0 amu
46.0 amu

30.1 amu
30.1 amu

39.0 amu

Answer 1

To calculate the atomic mass of the hypothetical element Jovian, we use the relative abundances and mass numbers of its isotopes.

1. **Isotope Masses and Abundances**:
- Jovian-44: Mass = 44 amu, Abundance = 22.4% = 0.224
- Jovian-46: Mass = 46 amu, Abundance = 44.0% = 0.440
- Jovian-48: Mass = 48 amu, Abundance = 100% - (22.4% + 44.0%) = 100% - 66.4% = 33.6% = 0.336

2. **Calculating the Atomic Mass**:
To find the weighted average, we multiply each mass by its relative abundance and sum them up:

\[
\text{Atomic mass} = (44 \, \text{amu} \times 0.224) + (46 \, \text{amu} \times 0.440) + (48 \, \text{amu} \times 0.336)
\]

Performing the calculations:

- \( 44 \, \text{amu} \times 0.224 = 9.856 \, \text{amu} \)
- \( 46 \, \text{amu} \times 0.440 = 20.24 \, \text{amu} \)
- \( 48 \, \text{amu} \times 0.336 = 16.128 \, \text{amu} \)

Adding these together:

\[
\text{Atomic mass} = 9.856 + 20.24 + 16.128 = 46.224 \, \text{amu}
\]

3. **Conclusion**:
The best value to use as the atomic mass of Jovian, rounded appropriately, is **46.2 amu**.

The correct response is: **46.2 amu**.