Mass Spectra of Elements
Introduced| English |
|---|
| isotopes/ˈaɪsətəʊps/ |
| mass spectrum/mæs ˈspektrəm/ |
| average atomic mass/ˈævrɪdʒ əˈtɒmɪk mæs/ |
Weighing single atoms
- Not all atoms of one kind weigh the same.
- A machine can sort them by weight, one type at a time.
- The result is a bar chart of tiny peaks.
- Each peak reveals a hidden variety of the same atom.
Same atom, different weight
- Isotopes 同位素 are atoms of one element with different numbers of neutrons.
- They share the same chemistry but differ in mass.
- Chlorine, for example, comes as chlorine-35 and chlorine-37.
Two isotopes of the same element differ in the number of...
Isotopes share protons but differ in neutrons, hence in mass.
Reading the peaks
- A mass spectrum 质谱图 plots each isotope's mass against how common it is.
- The peak position gives the mass; the peak height gives the relative abundance.
- Two peaks mean two isotopes.
In a mass spectrum, the height of a peak shows the isotope's relative ____.
Peak height is the relative abundance; peak position is the mass.
The weighted average
- The average atomic mass 平均原子质量 is a weighted average of the isotopes:
- The more common isotope pulls the average toward its own mass.
- This is the value printed on the periodic table.
Build chlorine's isotopes
Change the number of neutrons to make Cl-35 and Cl-37 - the two peaks a mass spectrum shows.
An element is 60% of mass 10 and 40% of mass 11. Its average atomic mass (in u)?
$0.60(10) + 0.40(11) = 6.0 + 4.4 = 10.4\ \text{u}$.
The average atomic mass lies closer to the more abundant isotope.
A weighted average is pulled toward the isotope with the larger fraction.
An element has two isotopes of mass 20 and 22, each 50% abundant. Its average mass (in u)?
$0.5(20) + 0.5(22) = 21\ \text{u}$ -- exactly halfway when equally abundant.
Chlorine is 75% chlorine-35 and 25% chlorine-37.
- $\bar{m} = 0.75(35) + 0.25(37) = 26.25 + 9.25 = 35.5\ \text{u}$.
- This matches chlorine's periodic-table mass of $35.5$.
When computing a weighted average from percentages, you should first...
Use fractional abundances so the weights sum to 1.
Use fractional abundances ($0.75$), not percentages ($75$), unless you divide by 100 at the end. The average lands closer to the more abundant isotope and is exactly halfway only when the two are equally common. And isotopes differ in neutrons alone -- same protons, so the same element.
Isotopes are atoms of one element with different neutron counts, so different masses. A mass spectrum shows a peak per isotope (position = mass, height = abundance). The average atomic mass on the periodic table is the abundance-weighted average, pulled toward the most common isotope.