### Convert 1 amu to MeV

Solution:

1) Determine mass of 1 amu (in kg):

By definition, the mass of 1 atom of C-12 is 12 amu.

Therefore, the mass of one mole of C-12 atoms is, by definition, 12 g

Avogadro's Number is 6.0221409 x 1023 mol¯1

12 g/mol / 6.0221409 x 1023 mol¯1 = 1.9926468 x 10¯23 g (mass of one atom of C-12 in g)

(1.9926468 x 10¯23 g) (1 kg / 1000 g) = 1.9926468 x 10¯26 kg (mass of one atom of C-12 in kg)

1.9926468 x 10¯26 kg/atom / 12 amu/atom = 1.660539 x 10¯27 kg/amu (this is the mass of 1 amu)

2) Use Einstein's mass-energy equation to determine Joules in one amu:

E = mc2

E = (1.660539 x 10¯27 kg) (2.99792458 x 108 m/s)2

E = 1.49242 x 10¯10 kg-m2/s2 (this is Joules)

3) Convert J to eV, then MeV

1 eV = 1.60217733 x 10¯19 J

1.49242 x 10¯10 J / 1.60217733 x 10¯19 J/eV = 931494893 eV

(931494893 eV) (1 MeV / 106 eV) = 931.494893 MeV

Often, 931.5 MeV is the value used in problem solving.

4) 931.5 MeV is the energy in one amu. Is it possible to express the mass of one amu using MeV in some way? I'm glad you asked:

E = mc2

931.5 MeV = mc2

m = 931.5 MeV/c2

The use of 931.5 MeV/c2 for the mass of 1 u is wide-spread. So much so that the c2 is often not written and you must infer its presence by context.

5) To sum up:

1 u = 931.5 MeV (expressed as energy)

1 u = 931.5 MeV/c2 (expressed as mass)

In solving problems, you may see this unit:

931.5 MeV/u-c2

read it as 931.5 MeV/c2 per 1 u

By the way, if you look around the Internet, you will find values different than the 931.494893 value I calculated. This is because different authors will use values that they have rounded off differently than the ones I used.

For example, I used 1.660539 x 10¯27 kg for the mass of 1 amu. Often, you will see it as 1.66 x 10¯27 kg.

The cumulative effect of these rounding off decisions will be seen in slightly different answers from different authors.