For the past 130 years, the Kilogram as a unit of measurement was defined by the International Prototype Kilogram. This was replaced in 2019 by a fundamental physical constant, namely Planck’s constant. The re-definition of the Kilogram in terms of this new constant has been highly controversial, splitting scientists into two main camps. The Avogadro camp advocates that the re-defined Kilogram should be based on ‘counting the number of silicon atoms’ inside a perfectly round sphere of pure silicon, whilst the supporters of Planck’s constant want to base this on the measurement of forces with a device called a Kibble balance. This article critically analyses the scientific debate surrounding these two scientific proposals and provides a balanced account of the pros and cons of each approach for the re-definition of the Kilogram.
This article concludes with a series of findings on the debate over which constant is preferable and how it could have gone either way in terms of the scientific evidence provided as both fundamental constants constitute perfectly valid definitions. It also argues that the controversy is rooted in the philosophy of science and the societal and institutional acceptance of the new definition of the Kilogram.
Units of measurement are essential in our everyday lives because without them, physical laws cannot be communicated precisely. Standard units are needed when for example constructing buildings, as these are important for measuring out how wide a gap must be in metres for a frame to be put in place that will perfectly fit, or how heavy the ceiling structure is in tonnes for a beam to support it. This demonstrates the importance of having standard units in our society, and without them, there would be chaos in how we engineer or design things as shown by prominent real-world disasters. For example, in 1999, NASA lost its $125m Mars Orbiter because one team used metric units for a calculation; the other used Imperial units.
For measurements to be accurate, there needs to be a core definition of what the unit is defined by. In the last 130 years, the core definition of the Kilogram has been based upon the so-called “international prototype kilogram” (IPK), which is a cylinder of platinum-iridium held in an archive in Paris. There are several copies of the IPK distributed across the world to ensure that a kilogram is always the same kilogram everywhere.
However, as the IPK and the international copies are physical objects, they tend to deteriorate over time through atmospheric contamination. As a result, there have been small mass gains in the IPK and its copies, which are on the level of 50 micrograms per 100 years as shown in Figure 1 below. Despite this minor drift of the mass in copies of the IPK over time, it is not a major problem for the rest of society. However, industries and research areas such as drug development and precision engineering where precise measurements are crucial can be greatly affected as a result.
Figure 1 Mass increase of the IPK and all of the copies over time. As indicated these are on the order of 50 micrograms over 100 years. credit: Greg L. CC BY-SA 3.0
Due to the drift in mass, many scientists felt that the 130-year-old IPK definition was outdated and not fit for the current age. To have a more stable definition of the Kilogram, a new standard definition based on fundamental physical constants was introduced in 2019, and was accepted by the General Conference of Weights and Measures (CGPM). A fundamental physical constant is an unchanging physical concept based on the theories of physics such as the speed of light or earth’s gravitational field strength. Rather than using a physical object such as the IPK, an instrument called a Kibble balance is used in the new definition which measures the current in electromagnetic coils using Planck’s constant to measure mass. Originally called a “Watt” balance, the Kibble balance has now been named after its inventor Bryan Kibble at the National Physical Laboratory (NPL), UK.
Figure 2: NIST K20 replica of IPK and the Watt balance (Kibble balance). Credit J.L Lee/NIST, NIST.
The redefinition of the Kilogram has been a major paradigm shift for many scientists, and many news articles have been celebrating its success. However, the understanding of why the Kilogram must be redefined according to Planck’s constant is a question that has not been realised by many. By investigating the many approaches that have been used before this definition we can realise the huge complexity it has taken to arrive at a final decision and the many other candidates that have not been chosen. We can also ask why Planck’s constant as a definition was favoured above others, such as Avogadro’s constant. There have also been many disagreements within the scientific and metrology communities of which definition is best suited and not everyone seems to agree with the outcome. Hence, the key questions addressed in this article are: what is the source of the controversy surrounding the redefinition of kilogram? Can we accept the new definition of the kilogram based on Planck’s constant?
Developing a solid definition for a standard unit
The development of a new definition of the Kilogram has emerged from various theories, and experiments carried out throughout the years. Creating a new definition for any standard unit will require a solid backing that can fully replace the existing one. There are criteria that need to be fulfilled and the planned revision of SI units rested on the proposal to deﬁne the base SI units by ﬁxing the exact values of the corresponding fundamental physical constants such as h, e, k, and NA. For example, to replace the metre’s definition from a prototype bar of 1 metre to “the speed of light in a vacuum during the time interval of 1/299792458 of a second” will require sufficient precise evidence and accurate findings to support the concept of the new definition. This will involve realisation of the new definition by providing an evidence-based approach (mise en pratique) that explores the new concept and links back to the original definition as a new counterpart from what it was before. In the case of the Kilogram, this means adhering to a relative uncertainty of 2*10-8 when measuring Planck’s constant. As with any other new proposed unit definition there should be a ‘stability requirement’ as Bronnikov et.al. have stated which means that the new definition has to be compatible with existing units and that any institutions or scientists who use the new unit will not be greatly affected by the change. The new definition of the Kilogram has been successful in that it did not change the way people worked with it. For example, balances and old scales can still be used as before and do not have to be altered and developed to weigh the new Kilogram. There should also be minimal corrections and errors and more simplicity being produced when planning and creating a new unit definition. Bronnikov et. al. also stated that the Kilogram’s new definition does not fully meet the above criteria and hence its new definition can be improved.
Planck’s constant and the Kilogram
Most scientists appear to hold the view that the Kilogram should be redefined in terms of Planck’s constant. Planck’s constant is a fundamental physical constant that is widely used in physics and explains the quantum relation of a photon’s energy to its frequency. Planck’s constant is denoted by a small ‘h’ and has a numerical value of:
The accuracy and precision of measuring h has been steadily improving with improved designs of the Kibble balance. The Kibble balance works on the principle of electromagnets and current. It was first introduced in 1975 by Bryan Kibble in NPL(National Physical Laboratory), based on the Ampere balance concept with many improvements and has been used by many metrological institutes to redefine the Kilogram.
Figure 3: Kibble (Watt) balance at the NIST institute. Credit: J.L Lee/NIST
Operating principles of the Kibble balance
A normal balancing scale has a plate onto which the test mass is placed and weighed as shown in Fig 4 (left). The weight of the measured object is made equal to the masses that are being placed on the other side (plate) of the scale. The definition of the object’s mass is equal to that of the masses that are being used. A Kilogram block mass would typically be used to equate the object’s mass to this.
Figure 4: Balance of forces comparison of scale (left) and Kibble (right) balance
The Kibble balance uses a completely different principle when it comes to weighing the object. Instead of equalizing the test mass’s force and the Kg mass object, the Kibble balance uses electromagnetic forces to equal the force of the object being weighed (Figure 4). The electromagnetic force is produced by a coil directly below the measured object. Electrical current will be flowing into the coil that is placed inside a powerful magnetic field created by a permanent magnet.
Overall, the two physical quantities to consider when weighing the mass of the object is the strength of the magnetic field and the current (Figure 5) that is running through the coil. 3]] Due to the interference of the coil’s magnetic field with the magnetic field of the permanent magnet an upwards force is produced f which is proportional to the current.
This movement of the coil allows the Kibble balance to operate in two modes: the velocity and the weighing mode.
Figure 5 Components of the Kibble balance Credit: Steiner et. al. NIST.
In weighing mode, a test mass is placed on the balance as shown in Figure 6 and Figure 5  which exerts a downward force on the coil This force is equal to mass times the gravitational field strength of the earth The current in the induction coil will be adjusted until the upward force is proportional to the current on the coil and exactly equals the downward force of the object. Eventually, an equilibrium will be reached between the electromagnet and the object’s forces and the current will also be recorded. The gravitational force of the mass will be equal and opposite to the electromagnetic force produced by the coil; a simple equation is used in the process to calculate the weight of the object and the force on the coil.
(mg is the weight of the object or can be F force on the coil which is proportional to B the magnetic field strength, L the length of the wire and I the current in the coil)
Figure 6: The weighing mode of the balance and the coil behaviour when the test mass is placed above the coil. (Both forces from coil and weight are balanced and current recorded).
Due to weight and current being measured easily in this mode, the magnetic field strength and the length of the wire need to be measured in Velocity mode.
Velocity mode (cf. Figure 7) is the second mode that is used to mainly calibrate the balance after it has been used. The test mass is removed and the current to the coil is stopped. As this process happens, a motor (as shown on the right-hand side of the balance in Figure 7) is used to force and move the coil up and down the magnet at a constant velocity. A voltage will be induced by this process and this will be measured.
Figure 7 Kibble balance behaviour in velocity mode – the left-hand coil oscillated by the right-hand motor coil (voltage recorded)
Figure 8: The motion of the coil in velocity mode (left). Lasers track the motion of the coil via interferometry which creates interference patterns (right). Credit: (coil movement) NIST, (interference pattern) Greg L. CC BY-SA 3.0
The coil’s motion is tracked with the help of laser interferometry as shown in Figure 8. The various positions of the coil’s motion are measured to the accuracy of the wavelength of the laser light which ensures that the coil’s motion is constant.
As the distance from laser and coil changes, a detector records the interference patterns and counts the number of circles produced as shown in Figure 8. The number of fringes is also counted by measuring the velocity of the coil that is produced. Due to the constant velocity of the coil, the electromagnetic field strength can also be calculated easily.
Another simple set of equations can be derived from some of these measurements that link voltage, magnetic field strength, length and velocity as shown in Figure 8 as well:
Voltage is directly proportional to the ‘B’ magnetic field strength, ‘L’ length of coil wire and ‘v’ velocity. The second equation states that the voltage and current are proportional to the weight ‘mg’ and velocity ‘v’.
The magnetic field and length does not have to be measured directly as these are constant here.
Voltage and current however are measured using quantum electrical methods. Voltage is measured using superconducting materials in the coil and the current with the help of a resistor. Resistance also has a link to Planck’s constant. Planck’s constant is calculated and resistance is measured using the Quantum Hall Effect . The constants used to measure current and voltage in summary link to Planck’s constant in a long equation with mass.
Another method that was proposed and used to redefine the Kilogram was Avogadro’s constant, which is a number commonly used in Chemistry to find the number of atoms in a given amount. Avogadro’s number is denoted by NA and equals to:
NA= 6.023 x 1023
This method uses a perfectly round pure Si silicon crystal sphere as shown in Figure 9 to count the number of 28 Si atoms to help and determine Avogadro’s constant in relation to the kilogram. Silicon in the form of a perfectly ‘round’ sphere allows the exact dimensions of this material to be measured. The sphere is carefully crafted and polished by hand until it is ‘perfect enough’.
Figure 9: A perfect silicon sphere that is meticulously crafted and only contains one silicon isotope 28Si atoms. Credit: NIST
To count the number of atoms in this silicon sphere the density must first be calculated. A special method called hydrostatic weighing is used to determine this. The density is always the volume of the sphere divided by the mass of the sphere. The diameter of the sphere will be measured very accurately using laser interferometry. This involves measuring the phase difference between two interfering laser beams that give rise to a distinct interference pattern similar to that shown in Figure 8 (right).
Figure 10:Laser interferometer and topographic image to determine the diameter of the silicon sphere. Credit: CC BY 3.0
The sphere will be made from a larger sphere and this larger sphere will have to be ground down until the sphere is fine enough for the diameter to be measured. Laser interferometry then measures the gaps and provides an accurate measurement of the diameter of the silicon sphere as shown in Figure 10. This is then used in the equation shown below to get the volume from the diameter measured.
X-Ray crystallography will be used for determining the spacing of the silicon atoms in the sphere known as the ‘lattice constant’. After determining the spacing of the silicon sphere atoms, the number of atoms can be easily determined using Avogadro’s number as shown in Appendix B The number of silicon atoms approximately counted in this project was 2.15 *1025 silicon-28 atoms.
As the number of silicon atoms is counted using Avogadro’s constant, the number of carbon 12 atoms in 12 grams has a natural relationship to the Kilogram through the definition of the mole which also links the mass of an object and Avogadro’s constant (see derivation). As a result of this relationship, the Kilogram can also be defined according to Avogadro’s constant rather than Planck’s constant.
The definition of Planck’s constant may have had a substantial impact on society as being the most prominent definition that links an object’s weight to a fundamental physical constant. However, Avogadro’s constant could also provide a good definition for the Kilogram.
The above review indicates that it is generally agreed that we need a set of standard units as a reference for measurements. However, the nature of this has been highly controversial, even if this is based on fundamental physical constants.
Science as a field of study is always strongly evidence-based. However, even in the light of strong evidence, scientists seem to dispute that the re-defined kilogram should be based on ‘counting numbers of atoms (i.e., Avogadro’s constant)’ and instead be based on the measurement of forces (Planck’s constant). It appears that these two schools of thought mirror the disciplinary boundary between Chemistry (Avogadro’s constant) and Physics (Planck’s constant). There are many disagreements between these two camps, and both have devised complex scientific methods to ‘realize’ the new definition of the Kilogram. Below I analyse and discuss the origin of the controversy surrounding the redefinition of kilogram by drawing on the research review.
Planck’s constant and the Kilogram
The new definition of the kilogram based on Planck’s constant has been accepted internationally as a fundamental and accurate definition. Some communities of scientists have welcomed this new definition of the kilogram. This is based on the premise that Planck’s constant does not meet the criteria for achieving a high accuracy and low uncertainty in terms of its measurement. Despite this fact, scientists have developed many ways to reduce these uncertainties by improving the design/measurement set-up of the Kibble balance. The main advantage of the Kibble balance over the silicon sphere method lies in its greater potential for enhancing the accuracy through careful optimisation of the measurement parameters. This is in strict contrast to the silicon sphere method which relies on a better method for polishing a silicon sphere to reduce the measurement uncertainty. The Kibble balance as an instrument is very customisable, making it ideal for improvements. Even though the theory on the Kibble balance is more difficult to understand for everyone, it is easier and less resourceful to use than the silicon sphere method. There are currently only a small number of these ‘perfect’ silicon spheres available worldwide and more time is needed to mature the definition, from polishing the spheres to reducing the uncertainty of them. The Kibble balance, however, has made good progress in reducing the uncertainty of its measurements of Planck’s constant.
Planck’s constant is used universally for measuring other physical quantities. When describing concepts to define the Kilogram in terms of Planck’s constant such as the Quantum Hall effect for resistance and the Josephson Current Effect (as stated by Steiner et. al.), these are being used in conjunction with measuring and analysing the Kilogram. These quantum concepts link together the current to mass and the weight to the Kilogram overall. Planck’s constant can be seen as a fairly stable constant as it is used in many different approaches from quantum physics to photonics. Linking the Kilogram to a constant such as Planck’s constant will hence lead to a longer-lasting and proper stable definition. The Kilogram becomes more integrated mathematically due to the use it will have in science and theory, therefore making it have a more theoretical representation. This means, as a result, that the definition cannot ‘change in nature’ like a more physical representation of the kilogram, thus making it more constant and consistent with the abstract description. This could make the Kilogram much more universal compared to Avogadro’s constant, due to the further independence Plank’s constant has from physical objects, and the theoretical aspect the fundamental constant has.
Issues arising from Planck’s constant:
Planck’s constant, however, still has weaker cards to play when it comes to representing the definition of the Kilogram. The Kilogram is all about weighing the physical mass of the object, whereas Planck’s constant could be too abstract to represent the physical mass of an object.
During the development of the Kibble balance, there resulted in many designs which yielded different levels of accuracy in the measurement of Planck’s constant.
Despite many improvements in the measured uncertainty of Planck’s constant, there is still a high level of disparity between the uncertainties achieved when measuring Planck’s constant, ranging from 1.9 *10-8 (NRC WB 2014 balance from NPL) to 4.5 * 10-8 (NIST WB 2014). This illustrates the difficulties associated with introducing a new unit definition which can appear to be ‘inaccurate’ when making an international comparison. The situation with the inaccuracies of the Kibble balance is roughly analogous to the prototype Kilogram and associated mass changes with its copies. The more uncertainties exist from the different balances across the world, the more difficult it becomes to reach the goal of an unchanging and accurate definition. The differences between the balances in design can also contribute to this as international institutes try to compete to make a ‘more accurate’ Kibble balance and having different types of balances with varying values is abstractly similar to having copies of IPK with varying characteristics and weight. One could ,therefore, be tempted to argue that there is only limited gain from trying to eliminate the uncertainties because there will always be inaccuracies in the measurements conducted worldwide that need to be dealt with and improved on. Despite these challenges, many institutions around the world have come close to the recommended value of the Planck’s constant provided by the CPIM.
Avogadro’s constant and the Kilogram
One of the greatest advantages of the Avogadro project is the bridge it makes to the Kilogram that Planck’s constant struggles to achieve . It makes an incredibly good link with the Kilogram as a mole is being defined as “12 grams of carbon 12 atoms which can also have exactly 0.012 kg” (Mills et. al.). If the mole is defined exactly in terms of 0.012 kg and we equate this to the number of atoms in a silicon sphere the Kilogram therefore gets a much better fitting definition. It therefore follows that Avogadro’s constant is a much more organically developed definition that can be linked very easily with the Kilogram unit with limited uncertainty, thus making the kilogram have a well-fitting definition that can be used and understood much better. The definition of the Kilogram based on Planck’s constant, however, has a very conceptual link to the Kilogram. The mechanics behind how electromagnetism and weight are linked together are very indirect and can cause concern for accuracy and acceptability. To make a good definition for a standard unit, there would need to be a proper link to the mass of an object and how the Kilogram as a unit is used. Avogadro’s constant on the other hand also provides a meaningful definition of the Kilogram. It may seem that using a constant such as Avogadro’s constant, which better links to the physical makeup of the object, makes better scientific sense than trying to relate the Kilogram to the energy constant of a photon (Planck’s constant). This provides Avogadro’s constant with more credibility for being more consistent with using the number of physical atoms to connect the object’s physical mass as defined by the Kilogram unit.
Avogadro’s constant also has another advantage in that the silicon sphere will also be able to re-define the mole, as well as the Kilogram through the definition. The Avogadro project provides a way to ‘unite the standard units’ more than Planck’s constant as a result of redefining two standard units, namely the mole and the Kilogram. Based on this there are valid reasons to consider Avogadro’s constant as a good candidate for providing a valuable definition for the kilogram. Avogadro’s constant has so far achieved a relative uncertainty of 1.8*10-8, which is relatively similar to the uncertainty range for Planck’s constant from the kibble balance (Max value: 1.9*10-8 ). On the other hand, the uncertainty achieved by the Avogadro project is slightly narrower in range than the different range of values from Planck’s constant reached by the various Kibble balances themselves internationally. This, therefore, reconsiders the fact that Avogadro’s constant could have a smaller uncertainty variation than the Planck constant project. Although these two have similar uncertainty values, this slightly smaller uncertainty in Avogadro’s constant shows the potential that the definition could have had as it might have more feasibility in progress in reducing uncertainty, as a result of this aspect.
Issues arising from the Avogadro project:
One of the key grounds that makes Avogadro’s constant questionable is the time-consuming process it takes to make and develop these silicon spheres. As mentioned before, there are only a tiny number of these silicon spheres available. The use of the Kilogram as defined by Avogadro’s constant does have its pitfalls. The definition itself relies on a perfectly round silicon sphere which is difficult to achieve and has led to the question of whether a super round silicon sphere is possible. This may also have been the main reason why Avogadro’s constant has not been chosen as the key definition for the Kilogram as there is a large scope for ‘rounding’ accuracy errors. However, there are still compelling reasons for using Avogadro’s definition, especially considering the strong link it makes for the Kilogram with the link to Avogadro’s constant and the credibility this definition has. As a result of this, Avogadro’s constant could have been a substantial definition for the Kilogram as the progress of development of the Kibble balance and the silicon sphere are relative to each other.
The meaning of an accurate definition
Planck’ versus Avogadro’s dispute is not purely rooted in scientific and technical issues. Science always strives for perfection and being as precise and accurate as possible. However, as Popper argues, scientific theories continuously evolve as scientists provide new evidence to refine concepts. Even for the fundamental constants, there are measurement uncertainties that can lead to errors that would need to be amended by more science and research. Hence, considering the many issues relating to the uncertainties in the silicon sphere and the Kibble balance method, developing and ‘perfecting’ the definition of the kilogram to make sure there are no loopholes for causing any issues in measurement can never be fully realised. From the viewpoint that the kilogram’s definition can become precise, it can never be 100 per cent accurate. As above there are still accuracy problems even with the new updated definition. This can relate to the issue that no matter how much development and time goes into redefining the kilogram there will never be a ‘perfect’ definition that society can base the kilogram on.
Effects on public education and acceptance:
Many would argue that the new definition of the Kilogram may not have an immediate impact on society as a whole. Indeed we are not going to see the Kibble balance replacing standard weighing instruments in the shops, however, at the conceptual level, many would see the re-definition of the Kilogram as a major ‘paradigm shift’ – from an easily understandable historic object of the IPK to a definition based on Planck’s constant.
As the definition of the Kilogram becomes more complex it would seem that only a few people and scientists would understand this new definition based on Planck’s constant. Hence the general population will need to be re-educated on the new definition based on Planck’s constant and information will need to be changed to reflect the new definition.
Further, here (Appendix) is a complete derivation of the equation for Planck’s constant and how this links to the mass of an object. It seems complex and difficult to understand for the general public.
Students would need to understand quantum concepts such as the quantum hall effect and an equation for the number of photons and electrons which links Planck’s constant along with understanding superconducting magnet principles. Simplifying and refining to make the definition clearer as suggested by Hill et al. would be a challenge when bringing out the definition to the wider general public, especially when explaining the Kilogram in this context where scientific understanding is needed to be able to apply the new definition. Based on this, there will be a widened gap between having a more elite type population who will understand and use these concepts, rather than the rest of the population. Conversely, if Avogadro’s constant were to be used there would have been some advantages; as Hill et al. stated that the definition of the Kilogram according to Avogadro’s constant is more “educationally appropriate” and can be considered to be more understandable than Planck’s constant.
However, to make the definition based on Planck’s constant more accessible and to help the younger generation to be more inspired and understand the mechanisms of how the Kilogram has been redefined in terms of Planck’s constants, Lego versions of the Kibble balance (Figure 12) were designed to be used as an educational tool. This not only gives more appreciation for Planck’s constant, but also demonstrates the difficulty involved in learning about and using the balance in practice..
Figure11: Lego Kibble balance from Southampton University, Department of Chemistry.
In sum, the above discussion indicates that the origins of the controversy are not only rooted in the disagreements between the two key camps of scientists who have devised complex scientific methods to ‘realize’ the new definition of the Kilogram, but also rooted in the philosophy of the science and institutional acceptance of the new Kilogram.
There are undoubtedly many compelling arguments for re-defining the Kilogram with the main reason being the mass fluctuations of the existing International Prototype Kilogram (IPK). The controversy surrounding this redefinition is about what replaces the IPK, and there were two strong competitors based on fundamental physical constants, i.e. Avogadro’s constant and Planck’s constant, which have been proposed and proven by the scientific community. The key question that remains is: can we accept the new definition of the Kilogram based on Planck’s constant? Based on the evidence provided, either Planck’s or Avogadro’s constants could have provided a robust SI definition, however Planck’s constant appears to be favoured by the scientific community. This is because the supporters of Planck’s constant have persuaded the community that this has the potential to reduce its measurement uncertainty via a highly customisable measurement set-up in the form of the Kibble balance. What is interesting to note from the two schools of thought is the fact that two different branches of science are being used with Physics being the focus of those who support Planck’s constant and Chemistry being at the centre of those who support Avogadro’s constant. Scientists from these two disciplines could have worked together to derive a unified definition in which Planck’s constant and Avogadro’s constant could have both been used. This would have eliminated any backlash from the scientific community on which definition is better.
Scientists try to assure the public that nothing will change in the way the kilogram operates as a unit as there is only a ‘change to its definition’. Despite this convincing argument the underlying controversy on scientific issues will continue and the general population will find it challenging to understand the scientific rationale for the definition. This is important for societal acceptance of the new definition of the kilogram overall. By considering the divisions created within the scientific community as a result of the Kilogram’s redefinition, and the difficulty associated with its societal acceptance and the wider implications for the way we think about creating units and measuring things, there needs to be more thought given to this in the future. The current definition of the kilogram for the moment is accurate and precise enough to be broadly accepted. Even Avogadro’s constant would have been sufficient for the redefinition of the kilogram and would have had broader appeal for the general population. It is ,therefore, expected that as science evolves, new definitions may evolve which would eventually supersede existing units such as the kilogram for weighing.
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I would like to thank my supervisor Sue Cavey from Peter Symonds College for her helpful guidance and support, and my scientific advisor Professor Jeremy Frey from the University of Southampton for his insightful comments and suggestions . It was a lot of fun to get the Lego Kibble balance working and learning through this experience.
Derivation of the equation for Planck’s constant
Derivation of the equation for Avogadro’s constant
a fundamental physical constant that relates the amount of energy a photon carries with the frequency of its electromagnetic wave (the energy of a quantum of electromagnetic radiation divided by its frequency, with a value of 6.626 × 10−34 joule-seconds) ↑
Avogadro constant – a fundamental physical constant that relates the number of atoms or molecules in a mole of a substance, equal to 6.022 52 × 1023 ↑
Methods set out by the international Bureau of Weights and Measures on how the SI unit may be realised ↑
When a magnetic field is applied perpendicularly to a metal strip electrons will collect on both ends and generate a voltage. As the applied magnetic field is changed the voltage changes in jumps ie. is quantised and so is the electrical resistance. This effect is called the quantum hall effect and it enables the precise measurement of the electrical resistance which is proportional to the charge of the electron and Planck’s constant. ↑
is a technique for measuring the density of an object based on Archimedes’ principle which states that an object will displace its own volume of water ↑