Isotopes and Mass Spectrometry Notes

Structure of the Atom

• Subatomic Particles:

  • Protons, neutrons, and electrons.

  • Protons and neutrons are located in the nucleus.

  • Electrons are found in quantum shells (energy levels).

• Relative Mass:

  • Proton: 1

  • Neutron: 1

  • Electron: $\frac{1}{1840}$ (or $\frac{1}{1836}$)

• Charge:

  • Proton: Positive (+1)

  • Neutron: Neutral (0)

  • Electron: Negative (-1)

Atomic Number and Mass Number

• Atomic Number:

  • Number of protons in an atom.

• Mass Number:

  • Number of protons plus the number of neutrons in an atom.

Isotopes

• Definition:

  • Atoms of the same element with the same atomic number but a different mass number.

  • Same number of protons, different number of neutrons.

• Example:

  • Chlorine-35 and Chlorine-37.

    • Both have the same number of protons and electrons.

    • Chlorine-35 has 18 neutrons.

    • Chlorine-37 has 20 neutrons.

• Important Note:

  • When explaining isotopes, refer to protons and neutrons or atomic number and mass number based on the question's requirements.

Relative Atomic Mass

• Definition: The weighted mean average mass of an atom of an element compared to one-twelfth of the mass of carbon-12.

• All atomic masses are measured relative to carbon-12, which serves as the standard.

• Takes into account the average of all isotopes of an element.

Relative Isotopic Mass

• The mass of a particular isotope relative to one-twelfth of the mass of carbon-12.

• Example: Mass of chlorine-35 or chlorine-37.

• Both relative isotopic masses and percentage abundances of isotopes are used to calculate the relative atomic mass.

Calculation of Relative Atomic Mass

• Multiply the relative isotopic mass by its percentage abundance for each isotope.

• Sum these values and divide by 100.

• Example: Lithium

  • Isotopes: Lithium-6 (6.015), Lithium-7 (7.016)

  • Abundances: 7.59%, 92.41%

  • $\text{Relative Atomic Mass} = \frac{(6.015 \times 7.59) + (7.016 \times 92.41)}{100} = 6.94$

Mass Spectrometry

• History:

  • First mass spectrometer built in 1918 by Francis Aston, a student of J.J. Thomson (discoverer of the electron).

  • Used to prove the existence of isotopes.

• Basic Principles:

  • Particles are turned into positive ions.

  • Ions are accelerated and deflected using electric or magnetic fields.

• Mass-to-Charge Ratio (m/z):

  • The path of an ion depends on its mass-to-charge ratio.

  • Ions with large m/z values are deflected less.

  • Ions with small m/z values are deflected more.

• Detector:

  • Detects mass-to-charge ratios, indicating the mass of each isotope.

  • Different isotopes are deflected differently and detected at different points.

• Applications:

  • Initially used to identify isotopes.

  • Now used to calculate molecular masses and determine the structure of new compounds.

Components and Steps of a Mass Spectrometer

1. Vaporization:

   • The sample is vaporized into a gas.

2. Ionization:

   • The gas is ionized, creating positive ions (typically with a +1 charge).

   • The goal is to create +1 ions so that the mass-to-charge ratio is simply the mass.

3. Acceleration:

   • Ions are accelerated using an electric field.

4. Deflection:

   • Ions are deflected using a magnetic field.

5. Detection:

   • Ions are detected using electric or photographic methods.

Path of Isotopes in Mass Spectrometer

• Heavier isotopes have larger m/z values and are deflected less.

• Lighter isotopes have smaller m/z values and are deflected more.

• If an ion has a +2 charge, its m/z value is halved, leading to greater deflection.

Mass Spectrum

• Information Provided:

  • Positions of peaks: Give the mass of substances (atomic mass).

  • Peak intensity (peak height): Gives the abundance of each isotope.

• The highest abundance is scaled to 100%, and other values are scaled accordingly.

• The mass spectrometer automatically generates a spectrum with peaks and abundances labeled.

• Example: A mass spectrum with peaks at m/z = 79 (50.5%) and m/z = 81 (49.5%).

  • $\text{Relative Atomic Mass} = \frac{(50.5 \times 79) + (49.5 \times 81)}{100} = 79.99$

Mass Spectrum of Diatomic Molecules

• Diatomic molecules contain only two atoms.

• Mass spectrometry can determine the relative molecular mass of the element.

• Example: Chlorine ($Cl_2$)

  • Peaks at 70, 72, and 74 correspond to different isotopic combinations.

    • 70: $^{35}Cl - ^{35}Cl$

    • 72: $^{35}Cl - ^{37}Cl$

    • 74: $^{37}Cl - ^{37}Cl$

Understanding Peak Heights in Diatomic Molecules

• If $^{35}Cl$ has an abundance of 75% ($\frac{3}{4}$) and $^{37}Cl$ has an abundance of 25% ($\frac{1}{4}$):

  • Chance of selecting two $^{35}Cl$ atoms: $\frac{3}{4} \times \frac{3}{4} = \frac{9}{16}$

  • Chance of selecting two $^{37}Cl$ atoms: $\frac{1}{4} \times \frac{1}{4} = \frac{1}{16}$

  • Chance of selecting one $^{35}Cl$ and one $^{37}Cl$: $\frac{3}{4} \times \frac{1}{4} = \frac{3}{16}$. Since the order can be $^{35}Cl$ then $^{37}Cl$ OR $^{37}Cl$ then $^{35}Cl$, the total probability is $2 \times \frac{3}{16} = \frac{6}{16}$

• Ratio of peak heights: 9:6:1 for 70:72:74 peaks.

• $\text{Relative Molecular Mass} = \frac{(9 \times 70) + (6 \times 72) + (1 \times 74)}{16} = 71$

• This confirms that the relative atomic mass of chlorine is 35.5, as $\frac{71}{2} = 35.5$

Example Questions: Bromine ($Br_2$)

• Isotopes: Bromine-79 and Bromine-81.

• $^{79}Br$ and $^{81}Br$ have approximately 50% abundance each.

• Peaks:

  • 158: Two $^{79}Br$ atoms.

  • 160: One $^{79}Br$ and one $^{81}Br$ atom.

  • 162: Two $^{81}Br$ atoms.

• Because the abundance of $^{79}Br$ and $^{81}Br$ is the same, approximately 50% each, the ration of 158 : 160 : 162 is 1 : 2 : 1, resulting from $(\frac{1}{2} \times \frac{1}{2}) : 2 \times (\frac{1}{2} \times \frac{1}{2}) : (\frac{1}{2} \times \frac{1}{2})$.

Past Paper Question Example

• If the ion detected had lost two electrons, the m/z value of the peak would be halved.