Question about units, if the units are given in the equation or as

[rwooduk]

... part of the value?

first example:

v (MHz) = 110 B(nT) E^2 (GeV)

could someone confirm that when an equation is like this you simply change E into GeV before squaring it and making the calculation? slightly confused.

second example:

rest mass of a Pion is stated by Wiki as 139.57018(35) MeV/c^2, why is this? are there units of c^2? what if you want to use the mass in a calculation, do you divide 139MeV by the speed of light squared? not sure what to do with this.

Thanks for any help.

 

[HallsofIvy]

If E is given in "GeV" then squaring will give units of "GeV squared". Of course, they should then combine with whatever units you have for "B(nT)" to give the correct units for v.

MeV is a measure of a type of energy which has basic MKS units "kilogram meters per second squared" so that dividing by a speed, squared, like c^2, leaves mass units: kilograms.

 

[rwooduk]

If E is given in "GeV" then squaring will give units of "GeV squared". Of course, they should then combine with whatever units you have for "B(nT)" to give the correct units for v.

MeV is a measure of a type of energy which has basic MKS units "kilogram meters per second squared" so that dividing by a speed, squared, like c^2, leaves mass units: kilograms.

thanks for that!

so why is it given over c^2 and not in kilograms? and also if there is a calculation where the pion mass is multiplied by c^2, do the c^2's simply cancel?

thanks again.

 

[D H]

MeV is a measure of a type of energy which has basic MKS units "kilogram meters per second squared" so that dividing by a speed, squared, like c^2, leaves mass units: kilograms.

Correction: "kilogram meters per second squared" -- that's the Newton (i.e., units of force). Energy has dimensionality mass*velocity², or units of kilogram*meters squared / seconds squared.

so why is it given over c^2 and not in kilograms?

Metric units can be rather inconvenient in particle physics. Expressing mass in terms of energy/c² tells a much better story. For example, how much energy is released in an annihilation event? Expressing rest mass in energy/c² is much more informative than expressing it in kilograms. In fact, in mass is expressed in electron-volts rather than electron-volts/c²; that missing division by c² is implied.

 

[paranormal]

In both of these examples, the units are given as part of the value. This means that the units should be included in any calculations using the given values. In the first example, the units for E are given as GeV, so it should be converted to GeV before being squared and used in the calculation. In the second example, the units for the rest mass of a Pion are stated as MeV/c^2. This means that the value should be divided by the speed of light squared (c^2) in order to use it in a calculation. It is important to include the units in calculations to ensure that the final result has the correct units and is consistent with the given values.