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Atomic Mass Constant

23rd Jun 2019 @ 3 min read

Physical Chemistry

The atomic mass constant is used to define the atomic mass unit (or the unified atomic mass). It equals one atomic mass unit. The atomic mass unit is the standard unit used to quantify mass on the atomic scale. Also, the atomic mass unit, the unified mass unit, and the dalton are all synonymous units and are interchangeably used.

Definition of Atomic Mass Constant

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

The atomic mass constant is equal to one atomic mass unit (or one unified mass unit).

Symbol of Atomic Mass Constant

The symbol for the atomic mass constant is mu.

Note: m should be in lowercase because m in uppercase is the symbol for the molar mass constant (Mu).

Unit of Atomic Mass Constant

It has the unit of mass, kg.

Formula of Atomic Mass Constant

The above definition can be mathematically expressed as:

m_\text{u} =\frac{1}{12}m_{(^{12}\text{C})}

Also, the atomic mass constant equals one unified mass unit (1 u). So, we can modify the above equation as

m_\text{u} =1\,\text{u} =\frac{1}{12}m_{(^{12}\text{C})}

Values of Atomic Mass Constant

The approximate value of mu is 1.661 10−27 kg. The more precise values are mentioned 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}

Atomic Mass Constant, Molar Mass Constant, and Avogadro Constant

The atomic mass constant (mu) and the molar mass constant (Mu) are related by the Avogadro’s constant (NA).

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

According to the Committee on Data for Science and Technology (CODATA), the recommended value of Mu is 0.999 999 999 65(30) g mol−1. This number can be approximated to 1 g mol−1 for practical purposes. Thus, substituting Mu ≈ 1 in the above equation, we have

1\text{u} \approx \frac{1}{N_\text{A}} 1\text{u} \times N_\text{A} \approx 1

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