3.1.1.2 - Mass Number and Isotopes

Counting particles correctly

Atoms are described by two important numbers. The atomic number, also called the proton number, tells you how many protons are in the nucleus. The mass number tells you the total number of protons and neutrons in the nucleus.

The atomic number fixes the identity of the element. Any particle with 6 protons is carbon; any particle with 8 protons is oxygen. Changing the number of neutrons does not change the element, but changing the number of protons does.

From these definitions:

• number of protons = atomic number
• number of neutrons = mass number - atomic number
• number of electrons = number of protons for an atom, then adjusted for any charge on an ion

For ions, remember that charge comes from gaining or losing electrons only. The nucleus does not change when a simple ion forms. For example, an $\mathrm{^{27}_{13}Al^{3+}}$ ion has 13 protons, 14 neutrons, and 10 electrons.

The diagram below shows how each part of the nuclide notation tells you something different about the ion.

[DIAGRAM: asset_name: 1.1.2 - Mass Number and Isotopes - Diagram 1; asset_slug: 1.1.2 - Mass Number and Isotopes - Diagram 1; recommended_method: retained_png; description: Aluminium-27 ion notation with mass number 27, atomic number 13 and charge 3+.]

One common mistake is to subtract the ionic charge from the mass number. Do not do that. Charge only changes the electron count.

What isotopes are and why they exist

Isotopes are atoms of the same element with different numbers of neutrons. They have the same atomic number but different mass numbers.

A given proton number can occur with different neutron numbers. Some isotopes are stable and others are radioactive; stability is not part of the definition of an isotope. The proton number must stay the same for the element to stay the same, but the neutron number can vary.

Isotopes of the same element have very similar chemical properties because chemical reactions involve electrons, especially the outer-shell arrangement. Since isotopes of the same element have the same number of electrons, they react in the same way chemically. Their physical properties can differ because their masses are different.

For example, chlorine-35 and chlorine-37 both have 17 protons and 17 electrons, so they take part in bonding in the same way. However, they do not have the same mass, because one has 18 neutrons and the other has 20.

That same logic is why the explanation should mention electron arrangement rather than just saying "they are similar atoms". The chemical behaviour comes from the electrons, not from the neutron number.

The simple time of flight mass spectrometer

Mass spectrometry allows chemists to separate ions by their mass-to-charge ratio, written as $m/z$. The time-of-flight method measures how long ions take to cross a fixed distance under vacuum.

In a simple TOF mass spectrometer, the sequence is:

1. ionisation
2. acceleration
3. ion drift
4. detection
5. data analysis

The sample is first ionised to form positive ions. In electron impact ionisation, a gaseous sample is bombarded with high-energy electrons, which knock an electron out of an atom or molecule:

In electrospray ionisation, a sample dissolved in a volatile solvent passes through a fine needle at high voltage. Solvent evaporates from charged droplets, leaving gaseous ions. A molecule may gain a proton to form $\ce{[M + H]+}$, whose $m/z$ is one greater than the relative mass of M for a singly charged ion. This gentler technique is useful for large molecules that would fragment under electron impact.

A vacuum reduces collisions with gas particles, so the measured drift time reflects the ion's speed rather than repeated scattering. The ions are then accelerated by an electric field so that ions with the same charge are given the same kinetic energy.

This point matters. If all ions have the same kinetic energy, lighter ions must move faster than heavier ions:

The ions then pass into the flight tube and drift toward the detector. Because lighter ions travel faster, they reach the detector sooner. When ions hit the detector, they gain electrons and produce a small current. The size of the current depends on how many ions arrive, so it tells us about relative abundance.

The computer uses the flight times and detector signal to produce a mass spectrum. The horizontal axis shows $m/z$. The vertical axis shows relative abundance.

Exam questions often give you the kinetic energy and the flight-tube length and ask for a time of flight, or give you the time and ask you to deduce the mass of an ion. The equations are supplied in the question; you need to combine them correctly.

Worked example: a $\ce{^{58}Ni+}$ ion is accelerated to a kinetic energy of $2.00 \times 10^{-16}\,\mathrm{J}$ and drifts along a $1.50\,\mathrm{m}$ flight tube.

• mass of one ion: $m = \dfrac{58}{1000 \times 6.022 \times 10^{23}} = 9.631 \times 10^{-26}\,\mathrm{kg}$
• speed: $v = \sqrt{\dfrac{2KE}{m}} = \sqrt{\dfrac{2 \times 2.00 \times 10^{-16}}{9.631 \times 10^{-26}}} = 6.444 \times 10^{4}\,\mathrm{m\,s^{-1}}$
• time: $t = \dfrac{d}{v} = \dfrac{1.50}{6.444 \times 10^{4}} = 2.33 \times 10^{-5}\,\mathrm{s}$

Running the steps backwards (time → speed → mass of one ion → mass of a mole of ions) lets you deduce the mass number of an unknown ion.

The diagram below shows the simplified TOF layout and why lower-mass ions reach the detector first.

[DIAGRAM: asset_name: 1.1.2 - Mass Number and Isotopes - Diagram 2; asset_slug: 1.1.2 - Mass Number and Isotopes - Diagram 2; recommended_method: retained_png; description: Time-of-flight stages: ionisation, acceleration, flight through a vacuum and detection; lighter ions of equal charge and kinetic energy arrive first.]

In low-resolution spectra, a singly charged ion has $m/z$ numerically equal to its mass number. That is why isotopes often appear at whole-number positions such as 20 and 22 for neon. More precisely, the instrument is measuring relative isotopic mass, which is not always an exact whole number.

Reading elemental mass spectra

Each isotope of an element produces a separate peak because each isotope has a different mass. The position of the peak tells you the $m/z$ value, and the height or area of the peak tells you the relative abundance.

This means a mass spectrum can identify an element. An element has a characteristic isotopic pattern. For example, chlorine has peaks at $m/z = 35$ and $m/z = 37$ in about a $3:1$ ratio. That pattern is distinctive.

To calculate $A_r$ from a simple elemental spectrum, use a weighted average:

Worked example: A sample of neon gives peaks at $m/z$ 20 and 22 with relative abundances 90 and 10.

The answer is not 21, because there are far more atoms of neon-20 than neon-22.

[DIAGRAM: asset_name: 1.1.2 - Mass Number and Isotopes - Diagram 3; asset_slug: 1.1.2 - Mass Number and Isotopes - Diagram 3; recommended_method: deterministic_code; description: Magnesium isotope spectrum: peaks at m/z 24, 25 and 26 with abundances 78.99, 10.00 and 11.01 percent.]

The vertical scale matters: a peak at 25 does not mean 25% abundance. Read its position from the horizontal axis and its abundance from the vertical axis.

When you interpret a spectrum, always link the peak positions to isotopes and the peak sizes to abundance. Students often describe the tallest peak as the heaviest isotope, but that is not always true. The tallest peak is simply the most abundant isotope.

Molecular ions and relative molecular mass

Mass spectrometry is also useful for finding relative molecular mass, $M_r$. For a singly charged molecular ion, its $m/z$ gives the relative mass of that molecular ion. A single molecular-ion peak is commonly used to estimate $M_r$ when one isotopic form dominates. If several isotopic forms give separate peaks, each peak is the mass of one isotopic combination, rather than the isotope-weighted mean $M_r$.

For an elemental sample, peaks usually come from isotopic ions of atoms. For a molecular sample, there may also be a molecular ion peak from the whole molecule. That peak can be used to estimate $M_r$; an isotope cluster must be interpreted with the isotopic composition in mind.

Chlorine provides a helpful pattern. Because chlorine has two common isotopes, $\mathrm{^{35}Cl}$ and $\mathrm{^{37}Cl}$, chlorine molecules can form three molecular-ion combinations:

• $\mathrm{^{35}Cl^{35}Cl^+}$ at $m/z = 70$
• $\mathrm{^{35}Cl^{37}Cl^+}$ at $m/z = 72$
• $\mathrm{^{37}Cl^{37}Cl^+}$ at $m/z = 74$

If the atomic abundance ratio is 3 : 1, the probabilities of selecting chlorine-35 and chlorine-37 are 3/4 and 1/4. The molecular probabilities are $(3/4)^2$, $2(3/4)(1/4)$ and $(1/4)^2$, giving a 9 : 6 : 1 pattern. The factor of two counts both possible orders for the mixed pair. This supports identification; it does not mean that a molecular peak is a weighted atomic mean.

When you read a spectrum, first decide whether the sample is an element or a molecule. That tells you whether to think about isotopic peaks of atoms, or a molecular-ion peak that can be used to read off $M_r$.

This kind of pattern recognition is powerful because it lets you move from raw peaks to a chemical conclusion very quickly.