Calculate Deutron Mass Given Binding Energy

[basenne]

Homework Statement

The deuteron is a bound state between a proton and a neutron (and the nucleus of the H2 isotope).

The binding energy of the deuteron is 2.2MeV. What is the mass of the deuteron?

Homework Equations

Mp = 938.3 MeV/c^2
Mn = 939.6 MeV/c^2

The Attempt at a Solution

Md = 938.3 + 939.6 - 2.2/c^2
= 1877.9 MeV


I tried to look for that number online, but I've only found numbers closer to 1875.7 MeV/c^2, which suggests to me that the binding energy changes the mass more than I found it to.

Where am I going wrong? Should I not be dividing the binding energy by c^2? Thanks for any help!

 

[TSny]

Md = 938.3 + 939.6 - 2.2/c^2
= 1877.9 MeV

Recheck this calculation.

[Note: The c^2 should not be dividing the 2.2. The c^2 appears in the units]

 

[basenne]

Can you explain to me how I can add quantities with differing units?

If I don't divide 2.2 by c^2, don't I end up with

MeV/c^2 + MeV/c^2 + MeV?

I was under the impression that you can't add differing units. Or do I have a fundamental misunderstanding somewhere?

Thanks, again!

 

[TSny]

The binding energy is 2.2 Mev. The mass equivalent of that is m = E/c² = (2.2 Mev)/c² = 2.2 Mev/c².

This now has the same units (Mev/c²) as you are using for the proton and neutron.