The kilogram is a key unit of mass that has been defined by a physical object—a metal cylinder stored in Paris—since 1799. However, this method has become problematic due to small changes in mass measurements over time. This article explores the efforts to redefine the kilogram using universal constants, moving away from relying on a physical object.
For over 200 years, the international prototype kilogram has been the standard for mass. However, precise measurements have shown that the mass of this prototype and various national standards have differed by about 50 micrograms. This inconsistency is not acceptable for a unit that is crucial to science and commerce. Moreover, the kilogram is the last of the base SI units still defined by a physical object, unlike the meter, which was redefined in 1983 based on the speed of light.
To redefine the kilogram, scientists aim to establish a standard based on unchanging constants of the universe. The two main approaches that have shown promise are:
1. **Using a Silicon Sphere to Determine Avogadro’s Number**
2. **Utilizing a Watt Balance to Determine Planck’s Constant**
Both methods strive to achieve agreement between the values obtained, reinforcing the reliability of the new definition.
The Watt balance, now known as the Kibble balance in honor of its inventor, Bryan Kibble, is a sophisticated device that measures Planck’s constant. It operates in two modes: weighing mode and velocity mode.
In weighing mode, a kilogram mass is placed on a pan attached to a coil of wire within a magnetic field. Current is passed through the coil until the electromagnetic force equals the gravitational force acting on the mass. The equation governing this balance is:
$$ text{Mass} times text{Gravity} = text{Magnetic Field} times text{Length of Wire} times text{Current} $$
In velocity mode, the mass is lifted off the pan, and the coil is moved through the magnetic field at a constant velocity. This motion induces a voltage in the coil, allowing for a second equation to be established:
$$ text{Voltage} = text{Magnetic Field} times text{Length of Wire} times text{Velocity} $$
By equating the two equations, scientists can eliminate variables that are difficult to measure precisely, leading to a relationship between electrical and mechanical power.
To connect the measurements from the Kibble balance to Planck’s constant, researchers use Josephson junctions. These junctions, made of superconductors separated by an insulator, generate a voltage when exposed to microwave radiation. The voltage produced is directly related to Planck’s constant, allowing for precise calculations.
Instead of measuring current directly, the Kibble balance measures voltage across a resistor, using the same Josephson junctions for accuracy. Resistance is measured using the quantum Hall effect, which provides a precise integer fraction related to Planck’s constant.
The culmination of these measurements and methods will lead to the redefinition of the kilogram in 2018. Instead of relying on a physical object, the kilogram will be defined based on the fixed value of Planck’s constant, ensuring consistency and precision in mass measurements worldwide.
The journey to redefine the kilogram represents a significant advancement in metrology, moving from a physical standard to one based on universal constants. This transition not only enhances the accuracy of mass measurements but also aligns the kilogram with the evolving standards of scientific measurement. As we approach this pivotal change, the collaboration between chemistry and physics underscores the importance of precision in our understanding of the universe.
Explore an online simulation of a Kibble balance. Adjust variables such as magnetic field strength and current to see how they affect the balance. Observe how these changes help in determining Planck’s constant. Reflect on how this method improves the precision of mass measurements compared to the traditional kilogram prototype.
Choose a universal constant, such as Avogadro’s number or Planck’s constant, and research its significance in redefining the kilogram. Prepare a short presentation explaining how this constant contributes to the new definition and its impact on scientific measurements.
Create a simple electromagnet using a battery, wire, and nail. Experiment with different wire lengths and battery voltages to observe changes in magnetic strength. Relate this to the principles of the Kibble balance and how electromagnetic forces are used to measure mass.
Engage in a classroom debate on the advantages and disadvantages of defining the kilogram by a physical object versus universal constants. Consider aspects such as precision, accessibility, and historical significance. Use evidence from the article to support your arguments.
Work through the equations used in the Kibble balance: $$ text{Mass} times text{Gravity} = text{Magnetic Field} times text{Length of Wire} times text{Current} $$ and $$ text{Voltage} = text{Magnetic Field} times text{Length of Wire} times text{Velocity} $$. Solve for unknown variables and discuss how these equations help eliminate measurement uncertainties.
Kilogram – The base unit of mass in the International System of Units (SI), equivalent to the mass of the International Prototype of the Kilogram. – The mass of the object was measured to be 2 kilograms using a balance scale.
Mass – A measure of the amount of matter in an object, typically measured in kilograms or grams. – The mass of the chemical sample was determined to be 0.5 kg.
Constants – Physical quantities that are generally believed to be both universal in nature and constant in time, such as the speed of light or Planck’s constant. – The speed of light, denoted as $c$, is a fundamental constant with a value of approximately $3 times 10^8 , text{m/s}$.
Planck – Referring to Max Planck, a physicist who originated quantum theory, or to Planck’s constant, a fundamental constant denoted as $h$. – Planck’s constant is used in the equation $E = h nu$ to relate the energy of a photon to its frequency.
Balance – An instrument for determining mass by comparing the mass of an object to known masses. – The chemist used an analytical balance to measure the precise mass of the reactants.
Voltage – The electric potential difference between two points, measured in volts. – The voltage across the resistor was measured to be 5 volts using a voltmeter.
Resistance – A measure of the opposition to the flow of electric current, measured in ohms. – According to Ohm’s Law, the resistance of a circuit is calculated as $R = frac{V}{I}$, where $V$ is voltage and $I$ is current.
Gravity – The force by which a planet or other body draws objects toward its center, measured as an acceleration of approximately $9.81 , text{m/s}^2$ on Earth. – The acceleration due to gravity affects the motion of falling objects, causing them to accelerate at $9.81 , text{m/s}^2$.
Measurements – The process of obtaining the magnitude of a quantity relative to an agreed standard. – Accurate measurements of temperature and pressure are crucial in determining the state of a gas.
Precision – The degree to which repeated measurements under unchanged conditions show the same results. – The precision of the instrument was evident as it consistently measured the length to within 0.01 cm.
