# Numerical value of physical constants Mathematica 10

Is there a way to use the physical constants in calculations and have Mathematica 10 figure out the final unit and numerical magnitude? When I try

pcM = N[Quantity[1, "PlanckConstant"]]


I simply get 1. h without the numerical value of Planck constant. Subsequently, using this in all further steps, keeps the answer in h and does not work out units.

However, if I define the Planck constant by hand and use it in a calculation, everything works as expected. I am curious as to why the internally defined constants do not show up with numerical values.

Thanks,

• what would you like the result to be, i.e. which units should it be with respect to? – chuy Aug 27 '14 at 15:19
• I learned just a few days ago that one can (often) use UnitConvert for this sort of thing. In:= UnitConvert[Quantity[1, "PlanckConstant"]] Out= Quantity[6.626070*10^-34, ( "Kilograms" ("Meters")^2)/("Seconds")] – Daniel Lichtblau Aug 27 '14 at 15:20
• or In:= UnitConvert[Quantity[1, "PlanckConstant"], "eV*s"] Out= Quantity[4.135668*10^-15, "Electronvolts" "Seconds"] – chuy Aug 27 '14 at 15:22

In physics, the Planck constant may be used as a natural unit.

If you want to switch to another unit system, use UnitConvert[].

For example, you can switch to standard SI units this way:

UnitConvert[Quantity[1, "PlanckConstant"], "SIBase"]


which will give you:

Quantity[6.626070*10^-34, ("Kilograms" ("Meters")^2)/("Seconds")]


This can be done at the end of calculation.

If you like to get rid of Quantity head, just do:

QuantityMagnitude[%]


which outputs:

6.626070*10^-34

• you can also use QuantityMagnitude to get the value out. – chuy Aug 27 '14 at 15:29
• @chuy, indeed, thank you! – Alexey Bobrick Aug 27 '14 at 15:31
• Or just UnitConvert without the second argument, which assumes SI units. – Mark Adler Aug 28 '14 at 3:40
• @MarkAdler: definitely right! Though, of course, using the second argument is a bit more general. For example, in engeneering applications one unit measure can be used and in spectroscopy - something totally different. – Alexey Bobrick Aug 28 '14 at 8:04

You should use the Physical Constants Package by using

<< PhysicalConstants


When you enter now

PlanckConstant


you directly get the Planck Constant. With

PlanckConstant/(Joule Second)
`

you get the Planck Constant without units.

• True, but note that PhysicalConstants package is obsolete and has been biult into Mathematica since version 9. – Alexey Bobrick Aug 27 '14 at 15:49