The dalton (symbol: Da), or unified atomic mass unit (symbol: u), is a unit of mass defined as of the mass of an unbound neutral atom of carbon-12 in its nuclear and electronic ground state and at rest.
The value serves as a conversion factor of mass from daltons to kilograms, which can easily be converted to grams and other metric units of mass. The 2019 revision of the SI redefined the kilogram by fixing the value of the Planck constant (), improving the precision of the atomic mass constant expressed in SI units by anchoring it to fixed physical constants. Although the dalton remains defined via carbon-12, the revision enhances traceability and accuracy in atomic mass measurements.
The dalton's numerical value in terms of the fixed-h kilogram is an experimentally determined quantity that, along with its inherent uncertainty, is updated periodically. The 2022 CODATA recommended value of the atomic mass constant expressed in the SI base unit kilogram is:<blockquote></blockquote> The previous 2018 CODATA value was used in the traditional definition of the Avogadro number to obtain the value , which was then rounded to 9 significant figures (thus guaranteeing continuity, to the precision indicated) and used to define it at exactly that value for the 2019 redefinition of the mole.
The mole is a unit of amount of substance used in chemistry and physics, such that the mass of one mole of a substance expressed in grams (i.e., the molar mass in g/mol or kg/kmol) is numerically equal to the average mass of an elementary entity of the substance (atom, molecule, or formula unit) expressed in daltons. For example, the average mass of one molecule of water is about 18.0153 Da, and the mass of one mole of water is about 18.0153 g. A protein whose molecule has an average mass of would have a molar mass of . However, while this equality can be assumed for practical purposes, it is only approximate, because of the 2019 redefinition of the mole.
Before the 2019 revision of the SI, experiments were aimed to determine the value of the Avogadro constant for finding the value of the unified atomic mass unit.
Josef Loschmidt
right|thumb|Josef Loschmidt
A reasonably accurate value of the atomic mass unit was first obtained indirectly by Josef Loschmidt in 1865, by estimating the number of particles in a given volume of gas. and relies on dissolving silver metal away from the anode of an electrolysis cell, while passing a constant electric current for a known time . If is the mass of silver lost from the anode and A the atomic weight of silver, then the Faraday constant is given by:
<math display="block">F = \frac{A_\text{r}M_\text{u}It}{m}.</math>
The NIST scientists devised a method to compensate for silver lost from the anode by mechanical causes, and conducted an isotope analysis of the silver used to determine its atomic weight. Their value for the conventional Faraday constant was = , which corresponds to a value for the Avogadro constant of : both values have a relative standard uncertainty of .
Electron mass measurement
In practice, the atomic mass constant is determined from the electron rest mass and the electron relative atomic mass (that is, the mass of electron divided by the atomic mass constant). The relative atomic mass of the electron can be measured in cyclotron experiments, while the rest mass of the electron can be derived from other physical constants.
<math display="block">\begin{align}
m_\text{u} &= \frac{m_\text{e{A_\text{r}(\text{e})}
= \frac{2R_\infty h}{A_\text{r}(\text{e}) c \alpha^2}
= \frac{M_\text{u{N_\text{A , \\[1ex]
N_\text{A} &= \frac{M_\text{u} A_\text{r}(\text{e})}{m_\text{e = \frac{M_\text{u} A_\text{r}(\text{e}) c\alpha^2}{2R_\infty h} ,
\end{align}</math>
where is the speed of light, is the Planck constant, is the fine-structure constant, and is the Rydberg constant.
As may be observed from the old values (2014 CODATA) in the table below, the main limiting factor in the precision of the Avogadro constant was the uncertainty in the value of the Planck constant, as all the other constants that contribute to the calculation were known more precisely.
{| class="wikitable"
|- style="line-height:133%"
! Constant
! Symbol
! 2014 CODATA values
! Relativestandarduncertainty
! Correlationcoefficientwith N
|-
| Molar mass constant
| align="center" |M
| 1 g/mol
| align="center" |0 (defined)
| —
|-
| Rydberg constant
| align="center" |R
|
| align="center" |
| −0.0002
|-
| Planck constant
| align="center" |h
|
| align="center" |
| −0.9993
|-
| Speed of light
| align="center" |c
|
| align="center" |0 (defined)
| —
|-
| Avogadro constant
| align="center" |N
|
| align="center" |
| 1
|-
|}
The power of having defined values of universal constants as is presently the case can be understood from the table below (2018 CODATA).
{| class="wikitable"
|- style="line-height:133%"
! Constant
! Symbol
! 2018 CODATA values
! Relativestandarduncertainty
! Correlationcoefficientwith N
|-
| Molar mass constant
| align="center" |M
|
| align="center" |
| —
|-
| Rydberg constant
| align="center" |R
|
| align="center" |
| —
|-
| Planck constant
| align="center" |h
|
| align="center" |0 (defined)
| —
|-
| Speed of light
| align="center" |c
|
| align="center" |0 (defined)
| —
|-
| Avogadro constant
| align="center" |N
|
| align="center" |0 (defined)
| —
|-
|}
X-ray crystal density methods
thumb|right|200px|[[Ball-and-stick model of the unit cell of silicon. X-ray diffraction measures the cell parameter, a, which is used to calculate a value for the Avogadro constant.]]
Silicon single crystals may be produced today in commercial facilities with extremely high purity and with few lattice defects. This method defined the Avogadro constant as the ratio of the molar volume, , to the atomic volume :
<math display=block>N_\text{A} = \frac{V_\text{m{V_\text{atom,</math>
where and is the number of atoms per unit cell of volume .
The unit cell of silicon has a cubic packing arrangement of 8 atoms, and the unit cell volume may be measured by determining a single unit cell parameter, the length of one of the sides of the cube. The CODATA value of for silicon is
In practice, X-ray crystallography measurements are carried out on a distance known as d(Si), which is the distance between the planes denoted by the Miller indices {220}, and is equal to .
The isotope proportional composition of the sample used must be measured and taken into account. Silicon occurs in three stable isotopes (Si, Si, Si), and the natural variation in their proportions is greater than other uncertainties in the measurements. The atomic weight for the sample crystal can be calculated, as the standard atomic weights of the three nuclides are known with great accuracy. This, together with the measured density of the sample, allows the molar volume to be determined:
<math display=block>V_\text{m} = \frac{A_\text{r}M_\text{u{\rho},</math>
where is the molar mass constant. The CODATA value for the molar volume of silicon is , with a relative standard uncertainty of
See also
- Mass (mass spectrometry)
- Kendrick mass
- Monoisotopic mass
- Mass-to-charge ratio
Notes
References
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