TheIBAxolotl
Inside the atom
An atom has a very small, dense, positively charged nucleus containing protons and neutrons (together called nucleons). Almost all of its mass is in the nucleus, but almost all of its volume is empty space occupied by electrons.
| Particle | Relative mass | Relative charge | Location |
|---|---|---|---|
| Proton | 1 | +1 | nucleus |
| Neutron | 1 | 0 | nucleus |
| Electron | about 1/1840 (≈ 0.0005) | −1 | around the nucleus |
Atomic number and mass number
- Atomic number, Z: number of protons. It defines the element.
- Mass number, A: protons + neutrons.
- Neutrons \(= A - Z\).
- Electrons in a neutral atom \(= Z\); in an ion, electrons \(= Z - \text{charge}\).
Nuclide notation writes A as a superscript and Z as a subscript before the symbol, e.g. \(^{37}_{17}\text{Cl}\).
Example: the ion \(^{32}_{16}\text{S}^{2-}\) has 16 protons, \(32-16 = 16\) neutrons and \(16+2 = 18\) electrons.
Isotopes
Isotopes are atoms of the same element (same Z) with different numbers of neutrons (different A).
- Same chemical properties, because chemistry depends on electron arrangement, which is identical.
- Different physical properties that depend on mass: density, rate of diffusion, and (slightly) melting and boiling points.
- Some isotopes are radioactive and have uses such as carbon-14 dating, cobalt-60 radiotherapy and iodine-131 tracers.
Relative atomic mass
The relative atomic mass, \(A_r\), is the weighted average mass of an element's atoms (taking natural isotope abundances into account) compared with one twelfth of the mass of a carbon-12 atom. It has no units.
\[A_r = \frac{\sum(\text{isotope mass} \times \text{abundance})}{\sum \text{abundances}}\]
Worked example 1
Chlorine is 75.78% chlorine-35 (mass 34.969) and 24.22% chlorine-37 (mass 36.966).
\[A_r = \frac{75.78 \times 34.969 + 24.22 \times 36.966}{100} = \frac{2649.95 + 895.32}{100} = 35.45\]
The answer lies closer to 35 because chlorine-35 is the more abundant isotope; a quick sanity check worth doing every time.
Worked example 2 (finding an abundance)
Boron has \(A_r = 10.81\) and two isotopes, \(^{10}\text{B}\) and \(^{11}\text{B}\). Let \(x\) be the fraction of boron-10.
\[10x + 11(1-x) = 10.81 \Rightarrow 11 - x = 10.81 \Rightarrow x = 0.19\]
So boron is about 19% boron-10 and 81% boron-11.
Mass spectra (HL)
A mass spectrometer turns atoms into positive ions and separates them by mass-to-charge ratio, m/z. For singly charged ions, m/z equals the isotope mass.
- Each peak = one isotope; peak height (or area) = relative abundance.
- To find \(A_r\): multiply each m/z by its relative abundance, add, and divide by the total abundance.
- For an element made of diatomic molecules such as Cl\(_2\), extra peaks appear at m/z 70, 72 and 74 from the combinations \(^{35}\text{Cl}^{35}\text{Cl}\), \(^{35}\text{Cl}^{37}\text{Cl}\) and \(^{37}\text{Cl}^{37}\text{Cl}\).
Common mistakes
- Adding instead of subtracting electrons for anions (or the reverse for cations).
- Dividing by the number of isotopes instead of by the total abundance.
- Giving \(A_r\) units (it has none; molar mass has g mol\(^{-1}\)).
- Saying isotopes react differently: their chemical properties are the same.
- Rounding isotope masses too early, which shifts the final decimal.
Exam tips
- Check that your \(A_r\) lies between the lightest and heaviest isotope and nearer the most abundant one.
- When abundances are percentages, divide by 100; when they are relative heights, divide by their sum.
- Count subatomic particles in a small table (p, n, e) to avoid slips.
- (HL) Read m/z values carefully off the spectrum axis; a missed small peak changes the answer.