Topic 1.2 Notes – Mass Spectra of Elements

1. Isotopes and Average Atomic Mass

Atomic number vs. mass number

• Atomic number (Z) = number of protons
  → This defines the element. If Z = 8, it’s oxygen. Always.
• Mass number (A) = protons + neutrons
  → This defines a specific isotope of that element.

If two atoms both have 17 protons, they’re chlorine.
If one has 18 neutrons and the other has 20 neutrons, they’re different chlorine isotopes.

What isotopes are

Isotopes:

• Have the same number of protons
• Have different numbers of neutrons
• Therefore have different mass numbers
• Have nearly identical chemical behavior (same electron configuration)

Chemical reactions depend on electrons, not neutrons. That’s why isotopes behave the same chemically but have different masses.

Why the periodic table shows a decimal

The atomic mass on the periodic table is not the mass of one atom.

It is the average atomic mass (AAM):

• A weighted average
• Based on the mass of each isotope
• Weighted by each isotope’s natural abundance

If one isotope is much more common, the average will be closer to its mass.

Weighted average formula

$$\text{Average atomic mass} = \sum (\text{isotope mass} \times \text{fractional abundance})$$

Important details:

• Convert percent to decimal first (82% → 0.82).
• All fractional abundances must add to 1.00.
• The answer must fall between the smallest and largest isotope masses.
• It will be closest to the most abundant isotope.

Quick example:

An element has:

• 10 amu (70%)
• 11 amu (30%)

$$(10)(0.70) + (11)(0.30) = 7.0 + 3.3 = 10.3 \text{ amu}$$

10.3 is between 10 and 11 and closer to 10. That makes sense.

Now let’s see how scientists actually get those numbers.

2. What a Mass Spectrum Shows

A mass spectrum is a graph showing the masses of isotopes and their relative abundances.

Here’s a simple example for a single element with three isotopes:

Example mass spectrum for one element

How to read it

• x-axis (m/z) = mass-to-charge ratio
  On the AP exam, assume:
  • Singly charged
  • Monatomic ions
  So m/z ≈ mass number.
• y-axis = relative abundance (often percent)

What each peak means

• Each peak = a different isotope
• Peak position → isotope mass
• Peak height → relative abundance
• Tallest peak → most abundant isotope, not the average mass

In the example above, the tallest peak is at m/z 24, so that isotope is the most abundant. The smaller peaks at 25 and 26 represent less common isotopes of the same element.

AP scope reminder:

• Only one element at a time
• Only singly charged monatomic ions
• No fragmentation or complicated organic spectra

3. From Mass Spectrum to Average Atomic Mass

When given a spectrum, you move from graph → weighted average.

Step-by-step

1. Read each m/z value → isotope masses.
2. Read each percent abundance.
3. Convert % → decimals.
4. Multiply mass × decimal abundance.
5. Add them.

Using the visual above:

$$(24)(0.75) + (25)(0.10) + (26)(0.15)$$

$$= 18.0 + 2.5 + 3.9 = 24.4 \text{ amu}$$

That’s the average atomic mass.

Without a calculator, estimate first. Since 24 is most abundant, the average must be slightly above 24. If your answer is 25.8, you made a mistake.

4. Solving for Unknown Abundance

Sometimes they flip it. You’re given:

• Two isotope masses
• The average atomic mass
• One abundance missing

You solve algebraically.

Setup

Let one abundance = $x$
The other = $1 - x$

Plug into:

$$\text{AAM} = (x)(m_{1}) + (1 - x)(m_{2})$$

Example structure:

$$35.6 = (x)(35) + (1 - x)(37)$$

Then solve for $x$.

Critical checks:

• Final answers must add to 1.00 (or 100%).
• Abundances cannot be negative.
• The isotope closer to the average must be more abundant.

On free-response questions, most mistakes come from forgetting that the abundances must sum to 1.

5. Connecting to the Periodic Table

The atomic mass printed on the periodic table comes directly from mass spectrometry data.

That decimal tells you:

• The element exists as a mixture of isotopes
• Those isotopes occur in specific natural abundances
• The value is a weighted average, not a single atom’s mass

Mass spectrometry is the experimental evidence behind those numbers.