System of units

The convention used here chooses units in which the numerical values of the reduced Planck constant, electron mass, elementary charge and

4 π

times the vacuum permittivity are one.

Hartree energy ( $E_{h}$ )

The atomic unit of energy,

E_{h} = ℏ^{2} / (m_{e} a_{0}^{2})

, approximately

27.2

eV. The hydrogen-atom ground-state energy is

- E_{h} /2

International System of Units

The International System of Units defines a common system for expressing physical quantities. Its base units include the kelvin for thermodynamic temperature; derived units combine them to describe quantities such as force and energy.^[ref]

SI prefix

An SI prefix supplies an exact decimal factor when attached to a unit of measurement. For example, milli means

1 0^{- 3}

and micro means

1 0^{- 6}

; a millimetre and a micrometre are correspondingly scaled metres. The prefix symbol and unit symbol form one unit that can itself be raised to a power.^[ref]

For an original conversion example,

2500 mm = 2500 \times 1 0^{- 3} m = 2.5 m, 4 m m^{2} = 4 (1 0^{- 3} m)^{2} = 4 \times 1 0^{- 6} m^{2} .

(1)

The area conversion squares the factor as well as the unit. Applying just one factor of

1 0^{- 3}

to that area would give

0.004 m^{2}

, a value 1000 times too large. Scientific notation makes the power explicit.

Prefix symbols are case-sensitive and cannot be stacked. For mass, prefixes attach to gram, because the base-unit name kilogram already contains a prefix. SI prefixes denote powers of ten, even in a computing context; they do not silently change into powers of two.^[ref] An exact unit conversion scales any stated measurement uncertainty with the value; it does not make an uncertain measurement exact.

Kilogram ( $kg$ )

The kilogram is the SI base unit of mass. The modern definition fixes the numerical value of Planck constant to

h = 6.62607015 \times 1 0^{- 34} J s

, with the metre and second defined through the other SI constants. It is no longer defined by the mass of a particular metal artifact.

A realization connects the defining constant to a practical mass measurement. That experiment has uncertainty even though the constant's defining numerical value is exact. The gram and milligram are decimal submultiples of the kilogram.^[ref]

Sievert ( $Sv = J k g^{- 1}$ )

The SI unit used for equivalent dose and effective dose. Sharing dimensions with the gray does not make the quantities interchangeable.^[ref]

Gray ( $Gy = J k g^{- 1}$ )

The SI unit of absorbed dose.^[ref]

Mole (unit, $mol$ )

The mole is the SI base unit of amount of substance. One mole contains exactly

6.02214076 \times 1 0^{23}

specified entities, as fixed by the Avogadro constant. It counts entities rather than a fixed mass or volume. ^[ref]

Newton (unit, $N$ )

The newton is the SI unit of force:

1 N = 1 kg m s^{- 2} .

(1)

This combines the units of mass and acceleration in Newton's second law. ^[ref].

Pascal (unit, $Pa$ )

The pascal is the SI unit of pressure:

1 Pa = 1 N m^{- 2} = 1 kg m^{- 1} s^{- 2} .

(1)

For a uniform normal force of

10 N

over area

0.02 m^{2}

, the pressure is

500 Pa

. The unit expresses a force per area, rather than the total force alone. ^[ref].

Joule ( $J = N m = kg m^{2} s^{- 2}$ )

The joule is the SI unit of energy, work, and heat. One newton of force acting along one metre of displacement does one joule of work. The relation

1 J = 1 N m

makes mechanical and electrical transfers comparable in the same energy unit. ^[ref]

Coulomb ( $C = A s$ )

The coulomb is the SI unit of electric charge. A constant electric current of

1 A

transports

1 C

in a time of

1 s

; a constant current of

2 A

for

3 s

transports

6 C

. The prefix in

1 nC = 1 0^{- 9} C

explains the much smaller charge scale used in the worked Coulomb's law example. ^[ref]

Volt ( $V = J/C$ )

The volt is the SI unit of electric potential and electric potential difference:

1 V = 1 J/C

, one joule per coulomb. A positive electric charge of

2 C

moved through a potential increase of

3 V

gains

Δ U = q ΔΦ = 6 J

of potential energy; the electric field does

- 6 J

of work. ^[ref].

Decibel ( $dB$ )