Unit 1 · Topic 1.2 Beta

Mass Spectra of Elements

Atoms of one element share an atomic number (protons) but can differ in neutrons; these isotopes have different masses.

Practice 4: Model AnalysisPractice 5: Mathematical Routines

Question set for this topic

Part 1 · Hook

Why this matters

Investigators can tell where a strawberry was grown, or whether honey was watered down with cane sugar, from tiny differences in the weights of its atoms. The tool is a mass spectrometer, which sorts atoms by mass. It also explains a puzzle on the periodic table: why chlorine's atomic mass is 35.45 when no chlorine atom weighs that.

Part 2 · Before you start

What this builds on

Part 3 · Prerequisite check

Quick check before you start

1. One atom of an element has a mass of 24.31 amu on average. What is the mass of one mole of its atoms?

  1. 24.31 g
  2. 24.31 amu
  3. 24.31 × 6.022 × 10²³ g
  4. 24.31 kg
Show the answer

The number in amu per atom is the same number in g per mole.

  • Correct: 24.31 g:
  • 24.31 amu:
  • 24.31 × 6.022 × 10²³ g:
  • 24.31 kg:

2. What is 60% of 70?

  1. 42
  2. 0.42
  3. 4200
  4. 116.7
Show the answer

60% is the fraction 0.60, and 0.60 × 70 = 42.

  • Correct: 42:
  • 0.42:
  • 4200:
  • 116.7:

Part 4 · See it

See it first

A mass spectrometer: atoms are ionized, accelerated, bent by a magnet (lighter ions bend more) and counted at a detector, giving a spectrum with a tall peak at 24 and smaller peaks at 25 and 26.
A mass spectrometer turns atoms into ions, sorts the ions by mass-to-charge ratio, and counts how many arrive at each mass. Each peak is one isotope. LevlPrep original diagram.

Part 5 · Step by step

How it works, step by step

  1. Atoms of one element all have the same number of protons but can have different numbers of neutronsan element can exist as several isotopes with different masses
  2. A mass spectrometer makes singly charged ions and sorts them by masseach isotope gives its own peak at its mass
  3. The height of each peak is proportional to how many atoms of that isotope are presentthe peak heights give the relative abundances
  4. Natural samples are a mix of isotopesthe atomic mass on the periodic table is the abundance-weighted average of the isotope masses

Part 6 · Key ideas

Key ideas

  • An atom has protons and neutrons in its nucleus and electrons around it. The atomic number (protons) identifies the element; the mass number = protons + neutrons.
  • Isotopes: same element, different numbers of neutrons, so different masses. ³⁵Cl and ³⁷Cl.
  • In a mass spectrum, each peak is one isotope (as a 1+ ion); its position is the mass and its height the relative abundance.
  • Average atomic mass = Σ (fraction × isotope mass). It sits closest to the most abundant isotope.

Part 7 · Misconception

A common mistake

The wrong idea: The atomic mass on the periodic table is the mass of a typical atom of the element.

What actually happens: It is a weighted average over the isotopes, and often no atom has exactly that mass. No chlorine atom has a mass of 35.45 amu; chlorine is about 76% chlorine-35 and 24% chlorine-37.

Part 8 · Check yourself

Check yourself

Exam-style questions. Anything you miss goes into your review queue.

1. What do all atoms of one element have in common?

  1. The same number of neutrons
  2. The same mass number
  3. The same number of protons
  4. The same mass, to the nearest 0.001 amu
Show the answer

The atomic number (number of protons) identifies the element. Neutrons, and so mass, can vary.

  • The same number of neutrons: Atoms of one element can differ in neutrons; those are isotopes.
  • The same mass number: Isotopes of one element have different mass numbers.
  • Correct: The same number of protons: Right: the number of protons, the atomic number, defines the element.
  • The same mass, to the nearest 0.001 amu: Different isotopes have different masses.

Graph

Mass spectrum of a pure element

A sample of a pure element is turned into singly charged positive ions (each atom loses one electron) and passed through a mass spectrometer. The isotope masses are 23.985, 24.986 and 25.983 amu.

020406080100242526Mass-to-charge ratio, m/zRelative abundance (%)
Data table
Mass-to-charge ratio, m/zElement sample
2478.99
2510
2611.01

2. How many isotopes of this element does the spectrum show?

  1. One, since the sample is a pure element
  2. Three
  3. Twenty-five, the middle mass
  4. Two, since the smaller peaks count as one
Show the answer

One peak per isotope: three peaks, three isotopes, with mass numbers 24, 25 and 26.

  • One, since the sample is a pure element: A pure element can still be a mix of isotopes; each peak is one.
  • Correct: Three: Right: each peak is ions of one isotope, and there are three peaks.
  • Twenty-five, the middle mass: The m/z values are masses, not a count of isotopes.
  • Two, since the smaller peaks count as one: The peaks at 25 and 26 have different masses, so they are different isotopes.

3. Calculate the average atomic mass of the element from the spectrum.

Type a number in amu.

Show the answer

(0.7899)(23.985) + (0.1000)(24.986) + (0.1101)(25.983) = 18.946 + 2.499 + 2.861 = 24.31 amu. Each mass is weighted by its fraction.

  • Answer: 24.31 amu

4. Which element is this, and what evidence supports the claim?

  1. Sodium, because the tallest peak is near 23
  2. Chromium, because three isotopes add to a mass near 75
  3. Aluminum, because 24 + 25 + 26 is close to 27 times 3
  4. Magnesium, whose atomic mass on the periodic table is 24.31
Show the answer

The abundance-weighted average, 24.31 amu, is the atomic mass of magnesium. An element is identified by matching its average atomic mass (and, with more data, its atomic number).

  • Sodium, because the tallest peak is near 23: The tallest peak is at 24, and sodium's average is 22.99, which does not match 24.31.
  • Chromium, because three isotopes add to a mass near 75: Atomic mass is a weighted average of the isotopes, not their sum.
  • Aluminum, because 24 + 25 + 26 is close to 27 times 3: A simple average of the mass numbers is 25, and aluminum's is 26.98: neither matches.
  • Correct: Magnesium, whose atomic mass on the periodic table is 24.31: Right: the weighted average, 24.31 amu, matches magnesium.

5. Why is the average atomic mass much closer to 24 than to 25?

  1. About 79% of the atoms are the isotope of mass 24
  2. The isotope of mass 24 has the most protons
  3. Heavier isotopes are not counted in the average
  4. The spectrometer detects lighter ions more easily
Show the answer

A weighted average sits nearest the most abundant isotope. Here 78.99% of the atoms have mass about 24.

  • Correct: About 79% of the atoms are the isotope of mass 24: Right: the most abundant isotope pulls the weighted average toward its mass.
  • The isotope of mass 24 has the most protons: Isotopes of one element have the same number of protons.
  • Heavier isotopes are not counted in the average: All isotopes count, each weighted by its abundance.
  • The spectrometer detects lighter ions more easily: The peak heights reflect how many atoms of each isotope are present, not a detector bias.

Data table

Isotopes of three elements

The table lists isotope masses and natural abundances.

Isotope data
ElementIsotopeIsotope mass (amu)Abundance (%)
Chlorine³⁵Cl34.96975.76
Chlorine³⁷Cl36.96624.24
Gallium⁶⁹Ga68.92660.11
Gallium⁷¹Ga70.92539.89
Boron¹⁰B10.013not given
Boron¹¹B11.009not given

6. A student says chlorine's mass spectrum would show one peak at 35.45, the atomic mass on the periodic table. Which response is correct?

  1. Yes, because the spectrometer reports the average mass of the atoms in the sample
  2. No; the spectrum shows peaks at 35 and 37 of equal height
  3. No; it shows one peak at 36, halfway between the isotopes
  4. No; it shows peaks near 35 and 37, the first about three times taller
Show the answer

The periodic-table value is a weighted average of real isotopes. The spectrum shows each isotope: a tall peak at 35 and one about a third as tall at 37.

  • Yes, because the spectrometer reports the average mass of the atoms in the sample: A mass spectrometer separates the isotopes and shows each one as a peak.
  • No; the spectrum shows peaks at 35 and 37 of equal height: The heights follow the abundances, 75.76% and 24.24%, about 3 to 1.
  • No; it shows one peak at 36, halfway between the isotopes: No chlorine atom has mass 36 in this data; the peaks are at each isotope's mass.
  • Correct: No; it shows peaks near 35 and 37, the first about three times taller: Right: 35.45 is an average. Each peak is a real isotope, and the heights follow 75.76% and 24.24%.

7. An atom of oxygen gains two electrons. What does it become?

  1. A cation with a 2+ charge
  2. An anion with a 2− charge
  3. An isotope of oxygen with a mass two units higher
  4. An atom of neon, which has two more electrons
Show the answer

O has 8 protons. With 10 electrons the charge is 8 − 10 = 2−: the oxide anion, O²⁻.

  • A cation with a 2+ charge: Gaining electrons adds negative charge; a cation forms when electrons are lost.
  • Correct: An anion with a 2− charge: Right: two extra electrons give two more negative charges than positive ones.
  • An isotope of oxygen with a mass two units higher: Electrons barely change the mass, and isotopes differ in neutrons, not electrons.
  • An atom of neon, which has two more electrons: The element depends on protons; oxygen keeps its 8 protons.

Part 9 · Summary

Summary

Atoms of one element share an atomic number (protons) but can differ in neutrons; these isotopes have different masses. A mass spectrometer sorts singly charged ions by mass, giving one peak per isotope, with heights showing relative abundance. The atomic mass on the periodic table is the abundance-weighted average of the isotope masses.

Part 10 · Up next

What comes next

Part 11 · Connections

Connections