Atomic Mass Unit (or Unified Mass Unit or dalton)

21st Jun 2019 @ 5 min read

The atomic mass unit is also known as the unified mass unit or the dalton. It is a standard non-SI unit of mass. It is used to quantify mass on the atomic scale, for example, the mass of a proton, the mass of an electron, the mass of iron.

Note: The atomic mass unit is now archaic. It is replaced by the unified mass unit or the dalton. But many institutions still continue to use the archaic name of the unit.

Definition and Formula of Atomic Mass Unit

The International Union of Pure and Applied Chemistry (IUPAC) defines the unified atomic mass unit as “one-twelfth of the mass of a carbon-12 atom in its ground state”.

One unified mass unit or one dalton is equal to one-twelfth of the mass of a neutral and unbound atom of isotopic carbon-12 at the ground state and at rest.

Symbol of Atomic Mass Unit

The symbol of the unified mass unit is u or amu.

Formula of Atomic Mass Unit

The above definition of the unified mass unit can be mathematically expressed as:

$1\,\text{u} =\frac{1}{12} \text{m}_{(^{12}\text{C})}$

Since, 1 u is the ¹∕₁₂ mass of carbon-12, we can say the mass of carbon-12 exactly equals 12 u.

$m_{(^{12}\text{C})} =12\, \text{u}$

Values of Atomic Mass Unit

The value of one unified mass unit approximately equals 1.661 × 10⁻²⁷ kg. More precise values of the unified mass unit are given below:

$1\,\text{u} &=1.660\,539\,066\,60(50)\times 10^{-27}\,\text{kg}\\ &=1.660\,539\,066\,60(50)\times 10^{-24}\,\text{g}\\ &=3.660\,861\,990\,69\times 10^{-27}\,\text{lb}\\ &=931.494\,095\,4(57)\,\text{ MeV}\big/c^2\\ &=1.822\,888\,486\times 10^3 \,m_\text{e}$

History

The history of atomic units goes back to 1803. This was a year when John Dalton used hydrogen, which is the lightest element, as a reference standard and calculated the relative atomic weight of other elements. Relative atomic weight does not have any unit; it is a dimensionless quantity.

At the beginning of the 20^th century, hydrogen was replaced by oxygen. And the atomic mass unit was defined as the one-sixteenth mass of an oxygen atom. During this period, the existence of isotopes was not known to scientists. Soon, it was discovered naturally occurring oxygen consists of three isotopes: ¹⁶O, ¹⁷O, and ¹⁸O. Physicists decided to define the atomic mass unit based on pure oxygen atom (¹⁶O) while chemists continue considering natural oxygen as a reference element. This led the confusion in the scientific community. To avoid this difference, scientific introduced carbon-12 as a common reference standard, replacing oxygen. Till today, carbon-12 continues to remain as an accepted reference element. Also, the atomic mass unit updated to the unified mass unit.

Atomic Mass Unit and Atomic Mass Constant

The atomic mass unit and the atomic mass constant m_u both are equal. The atomic mass constant is used to serve the atomic mass unit.

$1\,\text{u} =m_\text{u} =1.660\,539\,066\,60(50)\times 10^{-27}\,\text{kg}$

Atomic Mass Unit and Avogadro Constant

The atomic mass unit or the unified mass unit is a non-SI unit, and it is not a practical unit of mass. In chemical laboratories, chemists prefer more quantifiable units like g mol⁻¹. We can establish the relationship between the atomic mass unit and gram with the help of the Avogadro constant (N_A). The relationship between them is as follows:

$1\text{u} =\frac{M_\text{u}}{N_\text{A}}$

where M_u is the molar constant. And its value is 0.999 999 999 65(30) g mol⁻¹. This value for practical purposes can be approximated to 1 g mol⁻¹. Thus, we can have

$1\text{u} \approx \frac{1\,\text{g}\,\text{mol}^{-1}}{N_\text{A}}$

Examples

The mass of hydrogen atom is 1.007 825 u.
The rest mass of an electron is 5.485 8 ×10⁻⁴
The mass of a proton and a neutron is 1.007 28 u and 1.008 u respectively. As we can notice, the mass of a proton or a neutron nearly equal 1 u.
The dalton is common used units in reporting the weight of biomolecules, for example, the mass of the protein is 2.3 kilodaltons or 2.3 ku.

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