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.

 

[HalfLostAndSearching]

As a scientist, it is important to double check your calculations and make sure you are using the correct equations and units. In this case, the binding energy should be divided by the speed of light squared (c^2) in order to convert it to units of mass. However, you also need to account for the fact that the binding energy is a negative value, as it represents the energy released when the proton and neutron combine to form the deuteron. Therefore, the correct equation to use would be:

Md = Mp + Mn - |Eb|/c^2

Where |Eb| represents the absolute value of the binding energy. This will give you a more accurate result for the mass of the deuteron. It is also important to note that the mass of the deuteron is not a fixed value, as it can vary slightly depending on the specific isotope and its nuclear properties.