A newly discovered element consists of 2 isotopes, one with a mass of 9.5 and a relative abundance of 17.2% and another with a mass of 2.2 and a relative abundance of 82.8%. Determine the atomic weight of the new element.
0.172*9.5 + 0.828*2.2 = 3.4566
Note that atomic weights are weighted averages of the isotopes.
To determine the atomic weight of the new element, you need to calculate the weighted average of its isotopes.
1. Start by converting the relative abundances to decimals:
- Isotope 1: 17.2% = 0.172
- Isotope 2: 82.8% = 0.828
2. Multiply the mass of each isotope by its relative abundance:
- Isotope 1: 9.5 * 0.172 = 1.634
- Isotope 2: 2.2 * 0.828 = 1.8176
3. Sum up the values obtained in step 2:
- 1.634 + 1.8176 = 3.4516
4. Round the result to the appropriate number of significant figures.
Count the number of significant figures in the atomic mass values given for each isotope. In this case, the mass of 9.5 has two significant figures, and the mass of 2.2 has two significant figures as well. Therefore, the atomic weight should have two significant figures.
- Rounded to two significant figures:
- 3.4516 ≈ 3.5
Hence, the atomic weight of the new element is 3.5.