An international effort to re-define the kilogram in terms of a mathematical constant instead of it being based on a cylinder of high-grade metal locked in a vault in France has achieved a minor breakthrough, scientists have said.

The present definition of a kilogram goes back more than 125 years when a solid cylinder of platinum-iridium alloy was agreed by everyone to weigh precisely one kilo – it is now kept under lock and key at the International Bureau of Weights and Measures in Sevres.

However, the standard kilo is literally losing weight for some unexplained reason, probably related to the loss of gas locked inside it when the cylinder was made. As a result, scientists are no longer satisfied that this physical object is accurate enough of such a fundamental measurement and want to re-define it by 2018 in terms of a mathematical constant.

However, in order to do this they need to devise a way of estimating yet another constant, called Avogadro’s number, which is the number of discreet particles – molecules or atoms – in a “mole” of substance. A mole of water, for instance, is just a few teaspoons in volume but it contains approximately 6.022 by 10 to the power of 23 (1 with 23 zeros after it) molecules – Avogadro’s number – which is greater than the number of grains of sand in the world.

Giovanni Mana and colleagues of Italy’s National Institute of Metrology Research in Turin have now obtained what they believe to be the most accurate estimate of Avogadro’s number to date, which can now be used to quantify Planck’s constant and hence help to re-define the kilogram in purely mathematical terms.

Journal of Physical and Chemical Reference Data

In this way it was possible to calculate the number of atoms in the sphere by examining the ratio between the total volume of the silicon sphere and the volume occupied by each silicon atom, which they calculated by measuring the cubic cell.

They made a similar estimate in 2011, with an uncertainty of 30 atoms, but the latest estimate has an uncertainty of just 20 atoms. This gave an estimate of Avogadro’s number of 6.02214082(11) by 10 to the power of 23, where the parentheses represents the uncertainty of the last two digits.

“Prior to redefining the kilogram, we must demonstrate that the new realisation is indistinguishable from the present one, to within the accuracy of the world’s best balances,” Dr Mana said.

“Otherwise, when changing from the present definition to the new one, all users in science, industry and commerce must change the mass value of all the existing artefacts,” he said.

The researchers believe that a more precise definition of Avogadro’s number strengthens the definition of Planck’s constant and finaly leads science to a firmer mathematical definition of the kilo.

‘Base units’ of measurement

The kilogram is one of the seven “base units” on which all other units of measurement in science are derived. The other six are the metre, second, ampere, kelvin, mole and candela, measuring, respectively, length, time, electric current, temperature, chemical amount and light intensity.