Consider the mass spectrometer shown in Figure 2.11. Determine whether each of the following statements is true or false. If false, correct the statement to make it true: (b) The height of each peak in the mass spectrum is inversely proportional to the mass of that isotope.

Verified step by step guidance

1. 1. Understand the concept of a mass spectrometer: A mass spectrometer is an instrument that is used to identify the different kinds of isotopes present in a sample of an element. It does this by ionizing the atoms in the sample and then accelerating them through a magnetic field. The ions are deflected by the magnetic field to different extents depending on their mass-to-charge ratio. The ions are then detected and the relative abundance of each isotope is determined.
2. 2. Analyze the statement: 'The height of each peak in the mass spectrum is inversely proportional to the mass of that isotope.' This statement is suggesting that the heavier an isotope is, the smaller the peak in the mass spectrum will be.
3. 3. Evaluate the statement: The height of each peak in the mass spectrum is actually representative of the relative abundance of each isotope in the sample, not the mass of the isotope. Therefore, the statement is false.
4. 4. Correct the statement: A more accurate statement would be 'The height of each peak in the mass spectrum is proportional to the relative abundance of that isotope in the sample.'
5. 5. Remember: The position of the peak in the mass spectrum (along the x-axis) is determined by the mass-to-charge ratio of the isotope, not the height of the peak (along the y-axis).

Key Concepts

Mass Spectrometry

Mass spectrometry is an analytical technique used to measure the mass-to-charge ratio of ions. It involves ionizing chemical species and sorting the ions based on their mass. The resulting mass spectrum provides information about the composition and abundance of different isotopes in a sample.

Isotope Abundance

Isotope abundance refers to the relative amount of each isotope of an element present in a sample. In mass spectrometry, the height of each peak in the mass spectrum corresponds to the abundance of the respective isotope, with taller peaks indicating higher abundance, not inversely proportional to mass.

Mass Spectrum Interpretation

Interpreting a mass spectrum involves analyzing the peaks to determine the identity and relative abundance of isotopes. The position of each peak indicates the mass of the isotope, while the height reflects its abundance. Therefore, the statement in the question is false; peak height is directly proportional to isotope abundance, not inversely related to mass.