Atomic Mass Unit (u) - Unit Information & Conversion

Quick Answer

1 atomic mass unit (u) = 1.66054 × 10⁻²⁷ kg

Definition: Exactly 1/12 the mass of a carbon-12 atom

Also known as: Dalton (Da) — same unit, different name

Practical scale:

• Hydrogen atom: ~1 u
• Carbon-12 atom: exactly 12 u (by definition)
• Water molecule (H₂O): ~18 u
• Average protein: 50,000-100,000 u (50-100 kDa)

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Quick Comparison Table

Particle/Molecule	Mass (u/Da)	Mass (kg)
Electron	0.000549 u	9.109 × 10⁻³¹ kg
Proton	1.007276 u	1.673 × 10⁻²⁷ kg
Neutron	1.008665 u	1.675 × 10⁻²⁷ kg
Hydrogen atom (¹H)	1.008 u	1.674 × 10⁻²⁷ kg
Carbon-12 atom (¹²C)	12.0000 u (exact)	1.993 × 10⁻²⁶ kg
Water molecule (H₂O)	18.015 u	2.992 × 10⁻²⁶ kg
Glucose (C₆H₁₂O₆)	180.16 u	2.990 × 10⁻²⁵ kg
Hemoglobin protein	~64,500 u (64.5 kDa)	1.071 × 10⁻²² kg

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Definition

What Is an Atomic Mass Unit?

The atomic mass unit (symbol: u), also called the unified atomic mass unit or Dalton (symbol: Da), is a unit of mass used for expressing atomic and molecular masses.

Official definition: 1 u = exactly 1/12 of the mass of one unbound carbon-12 atom at rest in its ground state

Value in SI units: 1 u = 1.660 539 066 60 × 10⁻²⁷ kg (with uncertainty ±0.000 000 000 50 × 10⁻²⁷ kg)

Why Use Atomic Mass Units Instead of Kilograms?

Atomic and molecular masses in kilograms are extraordinarily small and unwieldy:

In kilograms (impractical):

• Hydrogen atom: 1.674 × 10⁻²⁷ kg
• Water molecule: 2.992 × 10⁻²⁶ kg
• Glucose molecule: 2.990 × 10⁻²⁵ kg

In atomic mass units (convenient):

• Hydrogen atom: 1.008 u
• Water molecule: 18.015 u
• Glucose molecule: 180.16 u

The atomic mass unit scales numbers to manageable sizes while maintaining precision for chemical calculations.

Carbon-12: The Reference Standard

Why carbon-12?

1. Exact definition: ¹²C is defined as exactly 12 u (no uncertainty)
2. Abundant: Carbon-12 comprises 98.89% of natural carbon
3. Stable: Not radioactive, doesn't decay
4. Central element: Carbon forms countless compounds, making it ideal for chemistry
5. Integer mass: Convenient reference point (mass = 12 exactly)

Historical context: Before 1961, physicists and chemists used different oxygen-based standards, creating two incompatible atomic mass scales. Carbon-12 unified them.

Dalton vs. Unified Atomic Mass Unit

Two names, same unit:

Unified atomic mass unit (u):

• Official SI-accepted name
• Used primarily in chemistry and physics
• Symbol: u

Dalton (Da):

• Alternative name honoring John Dalton
• Used primarily in biochemistry and molecular biology
• Symbol: Da
• Convenient for large molecules (kilodaltons, kDa)

Relationship: 1 u = 1 Da (exactly equivalent)

Usage patterns:

• "The oxygen atom has a mass of 16.0 u" (chemistry)
• "The antibody protein has a mass of 150 kDa" (biochemistry)

Both refer to the same fundamental unit.

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History

John Dalton and Atomic Theory (1803-1808)

John Dalton (1766-1844), an English chemist and physicist, revolutionized chemistry with his atomic theory (1803):

Dalton's key postulates:

1. All matter consists of indivisible atoms
2. Atoms of the same element are identical in mass and properties
3. Atoms of different elements have different masses
4. Chemical compounds form when atoms combine in simple whole-number ratios

Relative atomic masses: Dalton created the first table of atomic weights (1805-1808), assigning hydrogen a mass of 1 and expressing other elements relative to it:

• Hydrogen: 1
• Oxygen: 7 (incorrect; should be ~16, but Dalton thought water was HO, not H₂O)
• Carbon: 5 (incorrect)

Though Dalton's numerical values were often wrong (he didn't yet know correct chemical formulas), his conceptual framework established that elements have characteristic atomic masses.

Berzelius and Improved Atomic Weights (1810s-1820s)

Jöns Jacob Berzelius (Swedish chemist, 1779-1848) refined Dalton's work with meticulous experiments:

Achievements:

• Determined accurate atomic weights for over 40 elements by 1818
• Established oxygen = 100 as the standard (for convenience in calculation)
• Introduced modern chemical notation (H, O, C, etc.)

Berzelius' atomic weights were remarkably accurate, many within 1% of modern values.

Cannizzaro and Avogadro's Number (1860)

Stanislao Cannizzaro (Italian chemist, 1826-1910) resolved confusion about atomic vs. molecular weights at the Karlsruhe Congress (1860):

Key insight: Avogadro's hypothesis (1811)—equal volumes of gases contain equal numbers of molecules—allows distinguishing atomic from molecular masses

Result: By 1860s, chemists adopted consistent atomic weights based on oxygen = 16

The Oxygen Standard Era (1890s-1960)

Chemist's standard (1890s onward):

• Natural oxygen (mixture of ¹⁶O, ¹⁷O, ¹⁸O) = 16.0000 exactly
• Practical for analytical chemistry
• Used in atomic weight tables

Physicist's standard (1900s onward):

• Oxygen-16 isotope (¹⁶O) = 16.0000 exactly
• Used in mass spectrometry and nuclear physics
• More precise for isotope work

The problem: Natural oxygen is 99.757% ¹⁶O, 0.038% ¹⁷O, and 0.205% ¹⁸O

• Chemist's scale and physicist's scale differed by ~0.0003 (0.03%)
• Small but significant for precision work

Unification: Carbon-12 Standard (1961)

1960 IUPAP resolution (International Union of Pure and Applied Physics):

• Proposed carbon-12 as the new standard
• Physicist Alfred Nier championed the change

1961 IUPAC resolution (International Union of Pure and Applied Chemistry):

• Adopted carbon-12 standard
• Defined: 1 atomic mass unit = 1/12 the mass of ¹²C atom

Advantages of carbon-12:

• Unified physics and chemistry scales
• Carbon is central to organic chemistry
• Mass spectrometry reference (carbon calibration)
• Abundant, stable, non-radioactive

Notation evolution:

• Old: amu (atomic mass unit, ambiguous—which standard?)
• New: u (unified atomic mass unit, unambiguous—carbon-12 standard)

The Dalton Name (1960s-1980s)

1960s proposal: Several scientists suggested naming the unit after John Dalton

1980s acceptance: The name "Dalton" (Da) gained widespread use in biochemistry

1993 IUPAC endorsement: Officially recognized "Dalton" as an alternative name for the unified atomic mass unit

Modern usage:

• Chemistry/physics: Prefer "u" (atomic mass unit)
• Biochemistry: Prefer "Da" (Dalton), especially with kDa (kilodaltons) for proteins

Mass Spectrometry and Precision (1900s-Present)

Mass spectrometry (developed 1910s-1920s, refined continuously):

Thomson and Aston (1910s-1920s):

• J.J. Thomson and Francis Aston developed early mass spectrographs
• Discovered isotopes by precise mass measurement
• Aston won 1922 Nobel Prize in Chemistry

Modern precision:

• Mass spectrometry now measures atomic masses to 8-10 decimal places
• Essential for determining isotopic compositions
• Used to measure the carbon-12 standard with extraordinary accuracy

CODATA values: The Committee on Data for Science and Technology (CODATA) publishes official atomic mass unit values every few years, incorporating latest measurements:

• 2018 value: 1 u = 1.660 539 066 60(50) × 10⁻²⁷ kg

2019 SI Redefinition

Historic change: On May 20, 2019, the International System of Units (SI) was redefined based on fundamental physical constants rather than physical artifacts (like the kilogram prototype)

New kilogram definition: Based on the Planck constant (h = 6.626 070 15 × 10⁻³⁴ J·s, exact)

Impact on atomic mass unit: The atomic mass unit is now indirectly tied to fundamental constants through the kilogram's new definition, though it remains defined as 1/12 the mass of carbon-12

Practical effect: Minimal—atomic masses remain effectively unchanged, but now rooted in unchanging physical constants

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Real-World Examples

Subatomic Particles

Fundamental particles (masses in atomic mass units):

• Electron: 0.000548580 u (≈ 1/1836 of a proton)
• Proton: 1.007276467 u
• Neutron: 1.008664916 u

Key insight: Protons and neutrons are each approximately 1 u, making atomic masses roughly equal to the total number of protons and neutrons (mass number A)

Common Atoms

Hydrogen isotopes:

• ¹H (protium): 1.0078250 u — most common hydrogen (99.985%)
• ²H (deuterium): 2.0141018 u — "heavy hydrogen" (~0.015%)
• ³H (tritium): 3.0160493 u — radioactive, rare

Common elements (most abundant isotope):

• ⁴He (helium): 4.002603 u
• ¹²C (carbon-12): 12.000000 u (exact, by definition)
• ¹⁴N (nitrogen-14): 14.003074 u
• ¹⁶O (oxygen-16): 15.994915 u
• ³²S (sulfur-32): 31.972072 u

Simple Molecules

Diatomic molecules:

• H₂ (hydrogen gas): 2.016 u
• N₂ (nitrogen gas): 28.014 u
• O₂ (oxygen gas): 31.998 u
• Cl₂ (chlorine gas): 70.906 u

Common compounds:

• H₂O (water): 18.015 u
• CO₂ (carbon dioxide): 44.010 u
• CH₄ (methane): 16.043 u
• NH₃ (ammonia): 17.031 u
• C₆H₁₂O₆ (glucose): 180.156 u

Biological Molecules (in Daltons/kDa)

Small biomolecules:

• Amino acids: 75-204 Da (e.g., glycine = 75 Da, tryptophan = 204 Da)
• Nucleotides: 300-500 Da (DNA/RNA building blocks)
• Glucose: 180 Da

Proteins (typically measured in kDa):

• Insulin: 5.8 kDa (small hormone)
• Hemoglobin: 64.5 kDa (oxygen-carrying protein in blood)
• Albumin: 66.5 kDa (most abundant blood protein)
• Immunoglobulin G (IgG): 150 kDa (antibody)
• Titin: ~3,000 kDa (largest known protein, in muscle)

Nucleic acids:

• DNA (double helix): ~650 Da per base pair
• Human genome: ~2 × 10⁹ base pairs ≈ 1.3 × 10¹² Da (1.3 teradaltons!)

Large complexes:

• Ribosome: 2,500-4,500 kDa (protein synthesis machinery)
• Virus particles: 10,000-1,000,000 kDa (10-1,000 megadaltons, MDa)

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Common Uses

1. Atomic Weights and Periodic Table

The periodic table lists atomic weights (average masses) of elements in atomic mass units:

Example: Carbon:

• Natural carbon contains 98.89% ¹²C (12.0000 u) and 1.11% ¹³C (13.0034 u)
• Weighted average: 0.9889 × 12.0000 + 0.0111 × 13.0034 = 12.0107 u
• Periodic table lists carbon's atomic weight as 12.011 u

Why atomic weights aren't integers: Most elements are mixtures of isotopes with different masses, so the average is non-integer

Usage: Every stoichiometry calculation in chemistry depends on atomic weights expressed in u or g/mol (numerically equal)

2. Molecular Mass Calculations

Molecular mass = sum of atomic masses of all atoms in the molecule

Example: Glucose (C₆H₁₂O₆):

• 6 carbon atoms: 6 × 12.011 = 72.066 u
• 12 hydrogen atoms: 12 × 1.008 = 12.096 u
• 6 oxygen atoms: 6 × 15.999 = 95.994 u
• Total: 72.066 + 12.096 + 95.994 = 180.156 u

Molar mass connection: 180.156 u per molecule = 180.156 g/mol (numerically identical!)

3. Mass Spectrometry

Mass spectrometry measures the mass-to-charge ratio (m/z) of ions:

Technique:

1. Ionize molecules (add or remove electrons)
2. Accelerate ions through electric/magnetic fields
3. Separate by mass-to-charge ratio
4. Detect and measure abundances

Output: Mass spectrum showing peaks at specific m/z values (in u/e or Da/e, where e = elementary charge)

Applications:

• Determining molecular formulas
• Identifying unknown compounds
• Measuring isotope ratios
• Protein identification in proteomics
• Drug testing and forensics

Example: A peak at m/z = 180 for glucose (C₆H₁₂O₆ = 180 u, charge = +1e)

4. Protein Characterization (Biochemistry)

Biochemists routinely express protein masses in kilodaltons (kDa):

SDS-PAGE (sodium dodecyl sulfate polyacrylamide gel electrophoresis):

• Separates proteins by molecular weight
• Gels calibrated with protein standards of known kDa
• "The unknown protein band migrates at ~50 kDa"

Protein databases:

• UniProt, PDB (Protein Data Bank) list protein masses in Da or kDa
• Essential for identifying proteins by mass

Clinical diagnostics:

• "Elevated levels of 150 kDa IgG antibodies detected" (immune response)
• Tumor markers identified by protein mass

5. Stoichiometry and Chemical Equations

Stoichiometry: Calculating quantities in chemical reactions

Example: Combustion of methane: CH₄ + 2O₂ → CO₂ + 2H₂O

Molecular masses:

• CH₄: 16.043 u
• O₂: 31.998 u
• CO₂: 44.010 u
• H₂O: 18.015 u

Mass balance: 16.043 + 2(31.998) = 44.010 + 2(18.015) = 80.039 u (both sides equal, confirming conservation of mass)

Practical calculation: To produce 44 grams of CO₂, you need 16 grams of CH₄ and 64 grams of O₂

6. Isotope Analysis

Isotopes: Atoms of the same element with different numbers of neutrons (different masses)

Examples:

• ¹²C: 12.0000 u (6 protons, 6 neutrons) — 98.89% of natural carbon
• ¹³C: 13.0034 u (6 protons, 7 neutrons) — 1.11% of natural carbon
• ¹⁴C: 14.0032 u (6 protons, 8 neutrons) — radioactive, trace amounts

Applications:

• Radiocarbon dating: ¹⁴C decay measures age of organic materials
• Climate science: ¹³C/¹²C ratios in ice cores track ancient temperatures
• Medical tracers: ¹³C-labeled compounds track metabolic pathways
• Forensics: Isotope ratios identify geographic origins of materials

7. Nuclear Physics and Mass Defect

Mass-energy equivalence (E = mc²): Mass and energy are interconvertible

Mass defect: The mass of a nucleus is slightly less than the sum of its individual protons and neutrons

Example: Helium-4 (⁴He):

• 2 protons: 2 × 1.007276 = 2.014552 u
• 2 neutrons: 2 × 1.008665 = 2.017330 u
• Sum: 4.031882 u
• Actual ⁴He nucleus mass: 4.001506 u
• Mass defect: 4.031882 - 4.001506 = 0.030376 u

Interpretation: The "missing" 0.030376 u was converted to binding energy that holds the nucleus together

Calculation: 0.030376 u × c² = 28.3 MeV (million electron volts)

This is the energy released when helium-4 forms from protons and neutrons (nuclear fusion).

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Conversion Guide

Atomic Mass Units to SI Units

To Kilograms

Formula: u × 1.660 539 × 10⁻²⁷ = kg

Examples:

• 1 u = 1.6605 × 10⁻²⁷ kg
• 12 u (carbon-12) = 1.9927 × 10⁻²⁶ kg
• 180 u (glucose) = 2.9890 × 10⁻²⁵ kg

Mnemonic: 1 u ≈ 1.66 × 10⁻²⁷ kg (remember "1.66" and the exponent "-27")

To Grams

Formula: u × 1.660 539 × 10⁻²⁴ = g

Examples:

• 1 u = 1.6605 × 10⁻²⁴ g
• 18 u (water) = 2.9890 × 10⁻²³ g

To Electron Volts (Energy Equivalent)

Formula: u × 931.494 × 10⁶ = eV (electron volts)

Using Einstein's E = mc²:

Examples:

• 1 u = 931.494 MeV/c² (often written as "931.5 MeV")
• Proton (1.0073 u) ≈ 938.3 MeV/c²

Usage: Particle physicists express masses in MeV/c² or GeV/c² (gigaelectron volts)

Molar Mass Connection

Key insight: Atomic/molecular mass in u is numerically equal to molar mass in g/mol

Why? Avogadro's constant (6.022 × 10²³) and the definition of the atomic mass unit are chosen such that:

1 u per atom = 1 g/mol

Examples:

• Water: 18.015 u per molecule = 18.015 g/mol
• Glucose: 180.156 u per molecule = 180.156 g/mol
• Hemoglobin: 64,500 u per molecule = 64,500 g/mol

Practical calculation:

• 18 g of water contains 6.022 × 10²³ molecules (1 mole)
• Each molecule weighs 18 u

Common Prefixes for Large Molecules

Kilodalton (kDa): 1 kDa = 1,000 Da = 1,000 u

• Typical protein range: 10-500 kDa

Megadalton (MDa): 1 MDa = 1,000,000 Da = 1,000 kDa

• Large protein complexes, viruses

Gigadalton (GDa): 1 GDa = 1,000,000,000 Da = 1,000 MDa

• Chromosomes, very large molecular assemblies

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Common Conversion Mistakes

1. Confusing Atomic Mass Unit with Gram

The Mistake: Using u and grams interchangeably

Why It Happens: Molecular masses and molar masses have the same numerical value (e.g., water = 18 u or 18 g/mol)

The Truth:

• Atomic mass unit (u): Mass of individual atoms/molecules
• Gram (g): Macroscopic mass unit
• Conversion factor: 1 u = 1.6605 × 10⁻²⁷ kg = 1.6605 × 10⁻²⁴ g

Example error:

• "A glucose molecule weighs 180 grams" ✗
• Correct: "A glucose molecule weighs 180 u" ✓
• Also correct: "One mole of glucose weighs 180 grams" ✓

2. Mixing Up Molecular Mass and Molar Mass

The Mistake: Using "molecular mass" and "molar mass" as if they mean the same thing

Why It Happens: They have the same numerical value but different units

The Truth:

• Molecular mass: Mass of one molecule (units: u or Da)
• Molar mass: Mass of one mole (6.022 × 10²³ molecules) (units: g/mol)

Example:

• Water molecular mass: 18.015 u
• Water molar mass: 18.015 g/mol
• Same number, different meanings!

3. Forgetting Isotope Composition When Calculating Atomic Weights

The Mistake: Using mass numbers instead of isotopic averages for elements

Why It Happens: Assuming elements have integer atomic masses

The Truth: Most elements are mixtures of isotopes, giving non-integer atomic weights

Example:

• Wrong: Chlorine = 35 u (this is only ³⁵Cl, one isotope)
• Correct: Chlorine = 35.45 u (weighted average of ³⁵Cl and ³⁷Cl in natural abundance)

Impact: 35 vs. 35.45 causes ~1.3% error in calculations

4. Confusing "amu" with "u"

The Mistake: Thinking "amu" (atomic mass unit) is different from "u" (unified atomic mass unit)

Why It Happens: Older textbooks used "amu" before 1961 standardization

The Truth:

• Old amu (pre-1961): Could refer to oxygen-16 scale or natural oxygen scale (ambiguous)
• Modern u (post-1961): Unified atomic mass unit based on carbon-12 (unambiguous)
• Today: "amu" usually means the modern "u" (same thing)

Recommendation: Use "u" or "Da" to avoid confusion

5. Incorrect Dalton-to-Kilogram Conversion

The Mistake: Using incorrect conversion factors or wrong exponents

Why It Happens: The exponent −27 is easy to misremember

The Truth: 1 u = 1.6605 × 10⁻²⁷ kg (exactly, with more significant figures available)

Common errors:

• Using 10⁻²⁶ instead of 10⁻²⁷ (off by factor of 10!)
• Using 1.66 instead of 1.6605 (less precision)

Mnemonic: "27 is three times 9 (number of protons in three helium atoms); remember 10⁻²⁷"

6. Misunderstanding Mass Defect

The Mistake: Thinking the mass of a nucleus equals the sum of its proton and neutron masses

Why It Happens: Expecting simple addition to work

The Truth: The nucleus is slightly lighter than the sum of its parts

Reason: Mass is converted to binding energy (E = mc²) that holds the nucleus together

Example:

• 4 separate nucleons (2 protons + 2 neutrons): 4.03188 u
• Helium-4 nucleus (2p + 2n bound): 4.00151 u
• Mass defect: 0.03037 u → binding energy

Impact: Nuclear fusion and fission release energy from this mass difference

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