The current SI unit of mass i.e. Kilogram is defined as mass equal to the mass of 1 dm³ of water at its maximum density, approximately 4 °C. It is also defined as being equal to the mass of the International Prototype of the Kilogram (IPK). The IPK is made of a platinum alloy known as “Pt‑10Ir”, which is 90% platinum and 10% iridium (by mass) and is machined into a right-circular cylinder (height = diameter) of about 39 millimetres to minimize its surface area.

Figure 1: K20 IPK at National Institute of Standards and Technology.

The alloy is chosen due to its properties like extreme resistance to oxidation, extremely high density (almost twice as dense as lead and more than 21 times as dense as water). Satisfactory electrical and thermal conductivities, and low magnetic susceptibility. The IPK is just a cylinder which is used to define one of the most widely used units of measurement. Unlike definitions of other physical quantities such as meter defined as distance light travels in a vacuum during a time interval of   ¹⁄_299,792,458 of a second Kilogram is susceptible to variations due to physical interactions like scratches on prototype or oxidation etc. Even if the change is very small in the order of micrograms it matters over long duration as other physical quantities depend on this value. This is the main reason scientists are working on redefining the unit of mass in terms of numerical constants in order to make it universal and in accordance with other constants.

The stability of the IPK is crucial because the kilogram underpins much of the SI system of measurement as it is currently defined and structured. For instance, the newton is defined as the force necessary to accelerate one kilogram at one metre per second squared. If the mass of the IPK were to change slightly, so too must the newton by a proportional degree. In turn, the pascal, the SI unit of pressure, is defined in terms of the newton. This chain of dependency follows to many other SI units of measure. For instance, the joule, the SI unit of energy, is defined as that expended when a force of one newton acts through one metre. Next to be affected is the SI unit of power, the watt, which is one joule per second. The ampere too is defined relative to the newton, and ultimately, the kilogram. Redefinition will not make the kilogram more precise, but it will make it more stable. A physical object can lose or gain atoms over time, or be destroyed, but constants remain the same. And a definition based on constants would, at least in theory, allow the exact kilogram measure to be available to someone anywhere on the planet, rather than just those who can access the safe in France.

Now how did the researchers go about redefining the term? The CIPM’s (International Committee for Weights and Measures) committee on mass recommends that three independent measurements of Planck’s constant agree, and that two of them use different methods. First method is counting the atoms in two silicon-28 spheres that each weigh the same as the reference kilogram. This allows them to calculate a value for Avogadro’s constant, which the researchers convert into a value for Planck’s constant. Kilogram is expressed in terms of Planck’s constant, which relates a particle’s energy to its frequency, and, through E = mc², to its mass. This means first setting the Planck value using experiments based on the current reference kilogram, and then using that value to define the kilogram. Another method uses a device called a watt balance also known as Kibble balance to produce a value for Planck’s constant by weighing a test mass calibrated according to the reference kilogram against an electromagnetic force.

Figure 2: Silicon Sphere at NIST

Why is Planck’s constant of such importance in defining mass? The Planck constant is a fundamental constant of nature which sets a limit on the accuracy with which we can measure both the position and momentum of a physical system. It depends on the SI units of length, mass and time: the metre, kilogram and second, respectively. As the second and metre are defined by universal constants such as the speed of light, they can be used in conjunction with a fixed value of the Planck constant to redefine the kilogram. This would remove the need for the International Prototype Kilogram.

 

 

Figure 3: The Kibble balance or watt balance at NPL ( National Physical Laboratory).

 

Figure 4: Bryan Kibble and Ian Robinson working together
on the improved Kibble balance.

The proposed definition of Kilogram is: “The kilogram, symbol kg, is the SI unit of mass. It is defined by taking the fixed numerical value of the Planck constant h to be 6.626070040×10⁻³⁴ when expressed in the unit J⋅s, which is equal to kg·m²·s⁻¹, where the metre and the second are defined in terms of c and Δν_Cs.”

Where,

c = Numerical value of speed of light ;

Δν_Cs  = numerical value of the caesium frequency ΔνCs, the unperturbed ground-state hyperfine transition frequency of the caesium 133 atom, to be 9192631770 when expressed in the unit Hz, which is equal to s−1.