Structure 1.2.3 – Mass Spectra and Relative Atomic Mass

Mass Spectrum

• A mass spectrum is a graph produced by a mass spectrometer that shows the relative abundance of isotopes of an element against their mass-to-charge ratio (m/z).
• For atoms with a +1 charge (which is common in simple ionization), the mass-to-charge ratio is effectively equal to the mass number of the isotope.

 Purpose of Mass Spectrometry:

• Determine the number and abundance of isotopes of an element.
• Calculate the relative atomic mass \( A_r \) of an element from isotopic data.

Understanding a Mass Spectrum:

A typical mass spectrum for an element with multiple isotopes will show:

• Peaks: Each peak corresponds to an isotope.
• Height or intensity of peaks: Proportional to the relative abundance of the isotope.
• m/z value: The position of each peak on the x-axis corresponds to the mass number (for ions with +1 charge).

Monoatomic Elements

Diatomic Elements

 Example Interpretation:

If an element has two peaks at:

• \( m/z = 20 \), abundance = 75%
• \( m/z = 22 \), abundance = 25%

This tells us that the element has two isotopes: mass numbers 20 and 22, with $75\%$ and $25\%$ relative abundance respectively.

Calculating Relative Atomic Mass from Mass Spectrum:

Use the formula:

\( A_r = \frac{(a_1 \times m_1) + (a_2 \times m_2) + \ldots}{100} \)

• \( a_1, a_2, \ldots \): % abundances of the isotopes
• \( m_1, m_2, \ldots \): mass numbers of the isotopes

Operational Steps (Not Assessed but Helpful for Understanding):

Ionization – Making the Atoms Charged

• To analyze an atom in the mass spectrometer, it first needs to be converted into a positively charged ion.
• This is achieved by firing a high-energy beam of electrons at gaseous atoms. One of the atom’s electrons is removed, resulting in a positive ion.
• Purpose: Only charged particles can be manipulated and detected by the instrument.

Example: \( \text{X (g)} + \text{e}^- \rightarrow \text{X}^+ (g) + 2\text{e}^- \)

Acceleration – Giving the Ions Kinetic Energy

• Once ionized, the positive ions are accelerated through an electric field.
• This ensures all ions have similar kinetic energy as they enter the next section.
• Purpose: Equal speeds are important to accurately compare how ions behave based on their masses during deflection.

 Deflection – Separating Ions by Mass

• As the ions move through a magnetic field, they are forced to change direction.
• Lighter ions are deflected more easily, while heavier ions resist bending and are deflected less.
• Analogy: Imagine ions being like paper and coins in a wind tunnel – paper (lighter ions) flies off more easily, while coins (heavier ions) resist the airflow.
• The strength of the magnetic field is gradually increased during the process so that ions with different mass-to-charge ratios are sequentially deflected into the detector.

Detection – Measuring and Recording the Ions

• Ions that are perfectly deflected reach the detector.
• On impact, each ion picks up an electron, generating a small electrical current.
• The greater the number of ions hitting the detector, the stronger the signal produced.
• These signals are sent to a computer and used to create a mass spectrum graph showing the relative abundance of each ion.

 Continuous Sweep: The magnetic field is not static—it is gradually increased. As this happens, ions of different masses are detected at different times, allowing a complete spectrum to be generated from lightest to heaviest ions.

 Final Output – The Mass Spectrum:

• The spectrum is a plot of relative abundance (y-axis) versus mass-to-charge ratio \( m/z \) (x-axis).
• Each peak corresponds to an isotope, and the height of the peak reflects its relative abundance in the sample.