Improving Avogadro’s number to help redefine the kilogram

An international team of researchers working in support of an effort to redefine the kilogram have correlated two of the most precise measurements of a constant called Avogadro’s number, and have obtained an average value that can be used for future calculations.

Their research, published this week in the Journal of Physical and Chemical Reference Data, takes the incredibly large Avogadro’s number (which is approximately 6.022×10^23) and uses two different calculations to come up with a more precise value that can be used as part of the global effort to redefine the kilogram in terms of a fundamental constant by 2018.

Currently, the weight standard of the kilogram is a platinum-iridium cylinder, housed in the Bureau of Weights and Measures in Sevres, France, that is about the size of a golf ball. However, in order to globalize the measure, experts are moving to replace it, redefining the kilogram in terms of the Planck’s constant within the next three years.

Before this can happen, however, the researchers point out that it must be demonstrated that the new standard is indistinguishable from the present one to prevent scientists and other individuals from having to adjust the mass value of all of their existing tools and instruments. Since Planck’s constant can be derived from Avogadro’s number, that’s where they decided to start.

Using a pure silicon isotope to recalculate the constant

Before a new definition of the kilogram can be created, metrologists first need to ensure that the fixed value of Planck’s constant is as high quality as possible, and a more precise definition of Avogadro’s number will enhance the definition of this constant.

The authors responsible for the new paper has calculated Avogadro’s number several times in the past by counting how many atoms are in a one kilogram sphere of pure Si-28, a silicon isotope. Silicon forms cubic cells of eight atoms each time it crystallizes, and this makes it possible to calculate the number of atoms in the sphere by examining the ratio between total crystal volume and the volume occupied by each silicon atom, determined by measuring the cubic cell.

Earlier this year, the team behind the new study calculated a new value for Avogadro’s number with an uncertainty of less than 20 atoms per billion – a decrease from a 30-atom uncertainty in a value they calculated four years ago. For improved accuracy, both versions of the number were correlated, then averaged into a single value: 6.02214082(11)x10^23, where the number in parentheses represents the degree of uncertainty of the last digit in the result.

While Avogadro’s number will not be officially used to help define the new mass standard, counting atoms will serve as a valuable way to check the accuracy of the Planck’s constant-based definition, while also serving as a way to put the definition of the kilogram into practice.


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