Redefining the Kilogram

Question 1

Q7: What was the goal of the Avogadro Project?

Answer 1

A7: The goal was to use a silicon sphere to determine Avogadro’s number (the number of atoms in a mole) to redefine the kilogram.

Question 2

Q8: What challenge did the Avogadro Project face?

Answer 2

A8: The challenge was achieving sufficient accuracy in counting atoms and making a perfect spherical shape.

Question 3

Q9: What is Planck’s constant, and how does it relate to redefining the kilogram?

Answer 3

A9: Planck’s constant relates the energy of a photon to its frequency. It is used to redefine the kilogram by providing a universal constant not dependent on a physical object.

Question 4

Q10: How was the kilogram redefined in 2011?

Answer 4

A10: The kilogram was redefined based on a fixed value of Planck’s constant.

Question 5

Q11: What complementary methods were used to achieve the kilogram’s new definition?

Answer 5

A11: The silicon sphere approach (determining Avogadro’s number) and the watt balance approach (measuring Planck’s constant) were used.

Question 6

Q12: Why is the new definition of the kilogram considered an improvement?

Answer 6

A12: It is based on universal constants rather than a physical object, providing greater stability and precision.

Question 7

Q13: How is the new definition of the kilogram similar to the redefinition of the meter?

Answer 7

A13: Both definitions are based on fixing a fundamental physical constant: the speed of light for the meter and Planck’s constant for the kilogram.

Question 8

Q14: What is the value of Planck’s constant used for the kilogram definition?

Answer 8

A14: The value of Planck’s constant is
h = 6.62607015 × 10−34 kg m2 s

Question 9

Q: What is the primary purpose of the Kibble balance?

Answer 9

A: The Kibble balance is used to define the kilogram based on fundamental physical constants, specifically Planck’s constant, rather than a physical artifact.

Question 10

Q: How does the Kibble balance differ from traditional balances?

Answer 10

A: Traditional balances measure mass by comparing the gravitational force on an object to known weights, whereas the Kibble balance measures mass by balancing electromagnetic forces against gravitational forces.

Question 11

Q: Describe the two operational modes of the Kibble balance.

Answer 11

A:
Weighing Mode: Measures the mass by equating the gravitational force on a kilogram mass to the electromagnetic force generated by a current passing through a coil in a magnetic field.

Velocity Mode: Measures the voltage induced by moving the coil in the magnetic field, which allows for precise calculation of the magnetic field strength and length of the wire in the coil.

Question 12

Q: What equation is used to balance the gravitational and electromagnetic forces in the Kibble balance?

Answer 12

A: The equation is
𝑚⋅𝑔=𝐵⋅𝐿⋅𝐼

where 𝑚 is mass,

𝑔 is gravitational acceleration,

𝐵 is magnetic field strength,

𝐿 is length of wire,

and 𝐼 is current.

Question 13

Q: How does the Kibble balance address the challenge of measuring magnetic field strength and coil length?

Answer 13

A: By using the velocity mode to induce voltage, the Kibble balance creates two equations which can be solved to eliminate the variables for magnetic field strength and coil length.

Question 14

Q: What is the role of Josephson junctions in the Kibble balance?

Answer 14

A: Josephson junctions measure voltage very accurately and are used to balance the induced voltage in the coil by providing a precise voltage reference based on microwave radiation.

Question 15

Q: How is current indirectly measured in the Kibble balance system?

Answer 15

A: Current is measured indirectly by measuring the voltage across a known resistor and using the relationship

𝐼=V/R

where 𝑅 is the resistance.

Question 16

Q: What technique is used to measure resistance in the Kibble balance system?

Answer 16

A: The quantum Hall effect is used to measure resistance with high precision.

Question 17

Q: How did the definition of the kilogram change in 2019?

Answer 17

A: The kilogram is now defined by a fixed value of Planck’s constant, rather than a physical artifact, based on precise measurements using the Kibble balance.

Question 18

Q: What is the significance of the equation

h= 4⋅π ^2 ⋅m⋅g⋅v /f ^2 n

the context of the Kibble balance?

Answer 18

A: This equation relates Planck’s constant (h) to mass (m), gravitational acceleration (g), velocity (v), and frequency (f), and is used to calculate the kilogram based on these fundamental measurements.

Question 19

Q: How is the local gravitational acceleration measured for use in the Kibble balance?

Answer 19

A: A gravimeter is used to measure the local gravitational acceleration by dropping a corner reflector down a vacuum tube and measuring its acceleration via interferometry.

Question 20

Q: Why is precision in measuring velocity critical for the Kibble balance?

Answer 20

A: Precise measurement of velocity is crucial because it directly affects the accuracy of the induced voltage measurement, which is used to determine magnetic field strength and length of the wire.

Question 21

Q: What is the function of the silicon sphere in the context of measuring fundamental constants?

Answer 21

A: The silicon sphere is used for counting atoms with high precision, helping to define constants such as Avogadro’s number, but it does not directly define the kilogram.

Question 22

Q: How does the definition of the mole differ from other SI units?

Answer 22

A: The mole is defined as the amount of substance containing exactly

6.022×10 ^23

elementary entities, which can be atoms, molecules, or particles, and is not based on a physical object but a number.

Question 23

Q: How does the redefinition of the kilogram impact the SI system of units?

Answer 23

A: The redefinition ensures that the kilogram is based on a fundamental physical constant, Planck’s constant, making the unit more stable and reproducible, independent of physical objects.