The Atomic System of Units - Maple Help

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The Atomic System of Units

Description

• 

The atomic system is based on a unit of mass, the electron mass (approximately equal to 9.109389710-31 kilograms), a unit of charge, the electron (approximately equal to 1.6021773310-19 coulombs), a unit of action, the planck (equal to Planck's constant over 2π), and a unit of electric permittivity written as kappa0 (equal to 1.107c2 farads per meter, or one statfarad per centimeter, where c is the magnitude of the speed of light).

• 

By taking combinations of these four units, one can derive four units corresponding to the base dimensions length, mass, time, and electric current.

• 

To facilitate using atomic units, enter the command Units[UseContext](Atomic) so that the second, volt, and tesla refer to the atomic and not SI context.

• 

When used in conjunction with the UseSystem command, the atomic system sets the following units for the given dimensions.  All units have context Atomic.

Dimension Name

Unit Name

 

 

mass

electron_mass

electric charge

electron

action

planck

electric permittivity

permittivity

length

bohr

time

second

force

hartree/bohr

energy

hartree

power

hartree per second

electric current

electron per second

electric potential

volt

electric capacitance

square electron per hartree

electric field strength

volt per bohr

electric displacement

electron per bohr squared

electric dipole moment

electron bohr

electric polarizability

electron bohr squared per volt

magnetic permeability

electron_mass bohr per electron squared

magnetic flux

volt second

magnetic flux density

tesla

magnetic inductance

volt second squared per electron

magnetizing force

hartree per tesla bohr cubed

electric dipole moment

hartree per tesla

magnetic polarizability

hartree per tesla squared

Atomic Base Units

• 

All atomic base units have the context Atomic, including the second, where one atomic second is approximately  2.418884310-17 SI second.

Dimension Name

Unit Name

Unit Symbol

 

 

 

length

bohr

a0

mass

electron_mass

em

time

second

s

electric current

electron/second

e/s

Atomic Derived Units with Special Names and Symbols

  

All units have the context Atomic.

Dimension Name

Unit Name

Symbol

In Terms of Other Atomic Units

 

 

 

 

action

planck

h_bar +

em*a0^2/s

energy

hartree

E0

em*a0^2/s^2

electric permittivity

permittivity

kappa0

s^2*e^2/a0^3/em

electric potential difference

volt

V

E0/e

magnetic flux density

tesla

T

em/s/e

  

A plus sign (+) indicates an abbreviation.

Examples

convert1.0,'units','bohr','m'

5.29177208410-11

(1)

convert1.0,'units','secondAtomic','s'

2.41888432810-17

(2)

convert1.0,'units','hartree','J'

4.35974380610-18

(3)

convert1.0,'units','voltAtomic','V'

27.21138344

(4)

If infolevel is set to a greater integer (possible settings are 1 through 5), more detailed information about the computation method is displayed.

infolevel[Units]:=1:

convert3.25721,'system','C''m'2,'Atomic'

convert/system:   "converting to the units e/a0^2"

0.05692953990

(5)

convert5.2342110-10,'system','C'2'J','Atomic'

convert/system:   "converting to the units e^2/E0"

8.8897882781010

(6)

withUnits[Standard]:

Units[UseSystem]'Atomic'

Units[UseContexts]'Atomic'

Notes: 

– 

To enter a unit in 2-D Math input, select the unit from the appropriate Units palette. If the unit you want is not there, select unit and then enter the unit.

– 

In Maple 2015 and later versions, the double brackets around a unit are not displayed unless you are editing the unit.

2.532'a0''s'

2.532a0scontexts:-Atomic

(7)

2.532'a0''sSI'

2.532a0s

(8)

combine,'units'

convert/system:   "converting to the units a0/s[second:-contexts:-Atomic]"

6.12461511810-17a0scontexts:-Atomic

(9)

5'em''a0'2's'

5ema02scontexts:-Atomic

(10)

convert,'system'

convert/system:   "converting to the units h_bar"

5h_bar

(11)

's'

5E0

(12)

'a0'2

5emscontexts:-Atomic2

(13)

combine3.25323'F','units'

convert/system:   "converting to the units e^2/E0"

5.5252895701020e2E0

(14)

'm'

2.9238573101010κ0

(15)

See Also

convert/system, convert/units, evalf, infolevel, Units, Units/Index, Units/Standard, Units/Systems, Units[UseSystem]


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