## Physics Questions People Ask Fermilab

**What is a MeV in grams?**

What is a MeV in grams? In the unlikely event that I fuse a couple of hydrogen nucleii what is the weight lost by the system? My reference says it's 3.2 MeV but that's not helpful.

Hi,

Let us start with eV (electron-volt). It is an energy unit used in High-energy physics. A MeV is the Mega electron-volt, e.g. million times more than eV. One eV is defined as the energy, that an electron ( or an other single-charged(q=1.6*10^-19 Coulombs) particle) gains when it undergoes a potential difference of 1 Volt. In the International units ( SI units) 1eV corresponds to 1.6*10^-19 Joules.

According to Einstein's formula E=mc^2, energy is equivalent to mass (and vice versa), up to the c^2 constant. In SI units, mass is in kilograms , and the speed of light is 3*10^8 m/s.

Therefore, 1eV energy corresponds to

m=(1.6*10^-19 Joules)/(9*10^16 m/s)= 1.8*10^-36 Kg=1.8*10^-33 grams.

Then 3.2 MeV corresponds to 3.2*10^6*1.8*10^-33 grams=5.7*10^-27 grams. Just as an illustration , the 3.2 MeV mass is roughly 6 times more than the rest mass of an electron.

While we're at it can you give me E =mc^2 in meaningful units, with the proportionality constant?

Chuck Walbridge

Well, what is a meaningful unit? For me it is the units of the SI system, mass in kilograms, length in meters, current in amperes, time in seconds, ... .

Then energy in Joules = 9*10^16*mass in kilograms.

If you give me your favorite energy units, we can rewrite this equation by finding the right proportionality constant.

Bye Arnold

Back to Questions About Physics Main Page

- Last modified
- 04/28/2014
- email Fermilab