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What units are used after eV, MeV, GeV, etc, are divided by c^2?

by Juxtaroberto
Tags: c^2, electronvolt, mass
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Juxtaroberto
#1
Feb16-11, 07:41 PM
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I know that the mass of subatomic particles is usually given in electronvolts, and that c[tex]^{2}[/tex] is set to 1 so that we can say, "This particle has a mass of 13 eV." However, if you divide 13 eV by c[tex]^{2}[/tex], you get an answer, x. What units is this in?

Oh, also, what units do we use c in in the first place? km/s, m/s, mi/s?
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Drakkith
#2
Feb16-11, 08:00 PM
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I believe it is Kilograms or grams since that is the unit of mass. Cant say for the c.
jtbell
#3
Feb16-11, 08:40 PM
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Quote Quote by Juxtaroberto View Post
I know that the mass of subatomic particles is usually given in electronvolts
This is sloppy language which is unfortunately commonly used by physicists.

The electron-volt (eV) is a unit of energy, equal to 1.602e-19 joule.

When someone says "the mass of an electron is 511 keV" he really means, "the energy-equivalent of the mass of an electron is 511 keV" or "the rest-energy of an electron is 511 keV" or "the mass of an electron is 511 keV/c^2." Mathematically,

[tex]m_e c^2 = 511 \rm{ keV}[/tex]

Dividing through by c^2 we get

[tex]m_e = 511 \rm{ keV}/c^2[/tex]

so the eV/c^2 is a unit of mass, equal to (1.602e-19 J)/(2.998e8 m/s)^2 = 1.782e-36 kg.

To check this, 511 keV = 511 x 1000 x 1.782e-36 kg = 9.108e-31 kg which is indeed the mass of an electron in kg.

clem
#4
Feb17-11, 10:48 AM
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What units are used after eV, MeV, GeV, etc, are divided by c^2?

This language is fortunately commonly used by physicists.
There are several systems of units in which c=1 and is dimensionless.
(Distance in light-years and time in years is one.)
All of those systems are more useful than kg or joules in describing an electron.
jtbell
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Feb17-11, 11:22 AM
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Quote Quote by clem View Post
There are several systems of units in which c=1 and is dimensionless.
(Distance in light-years and time in years is one.)
I wouldn't call "light-years per year" dimensionless.


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