Calculate Deutron Mass Given Binding Energy

In summary: The deuteron mass is then Md = 938.3 Mev/c2 + 939.6 Mev/c2 - 2.2 Mev/c2 = 1875.9 Mev/c2.In summary, the deuteron is a bound state between a proton and a neutron, with a binding energy of 2.2 Mev. The mass of the deuteron can be calculated by adding the masses of the proton and neutron (938.3 Mev/c2 and 939.6 Mev/c2 respectively) and subtracting the binding energy (2.2 Mev/c2). This gives a mass of 1875.9 Mev/c2. However, further calculations may be needed to
  • #1
basenne
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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!
 
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  • #2
basenne said:
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]
 
  • #3
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!
 
  • #4
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.
 
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  • #5


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.
 

Related to Calculate Deutron Mass Given Binding Energy

1. What is the formula for calculating deutron mass given binding energy?

The formula for calculating deutron mass given binding energy is:
m = (E/c^2) * (1 - 1/(2*c^2) * (E/mc^2))
Where m is the deutron mass, E is the binding energy, and c is the speed of light.

2. How is the binding energy of a deutron related to its mass?

The binding energy of a deutron is directly related to its mass. This means that as the binding energy increases, the mass of the deutron also increases. This is because the binding energy is the amount of energy required to keep the particles in the nucleus together, and this energy contributes to the overall mass of the deutron.

3. What units are used to measure binding energy and deutron mass?

Binding energy is typically measured in electron volts (eV) or joules (J), while deutron mass is measured in kilograms (kg) or atomic mass units (u). In some cases, the energy may also be expressed in MeV (mega electron volts) or GeV (giga electron volts).

4. Can the formula for calculating deutron mass given binding energy be used for other particles?

Yes, the same formula can be used for other particles as long as they have a definite mass and binding energy. However, the values of c (speed of light) and m (particle mass) may vary for different particles, so the values used in the formula should be specific to the particle being calculated.

5. How is the calculated deutron mass related to the actual measured mass?

The calculated deutron mass is typically very close to the actual measured mass. This is because the formula takes into account the binding energy, which contributes to the overall mass of the deutron. However, there may be slight variations due to experimental errors or uncertainties in the values used in the formula.

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