Estimating Temperature of Universe at Deuteron Disassociation?

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In summary, the person is trying to estimate the temperature of the universe when it has cooled enough that photons no longer disassociate the deuteron. They used the Ionization Energy of the ground state of electron(13.6eV), and used the following approach: k=8.62e-5eV/K. When they tried to use the Ionization Energy of deuterium (14.9eV), they got a number that was really wrong. They realized that the number was about the total mass of deuterium, and they were able to solve the problem after understanding that the mass difference between a free proton and neutron and the deuterium bound state is times c^2.
  • #1
freefallin38
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Ok, I have this homework problem that is driving me nuts, and I only have a short period of time to get it. The question is, Estimate the temperature of the universe when it has cooled enough that photons no longer disassociate the deuteron. There was another part that asked for the temperature when the hydrogen atom is no longer dissociated. For that problem I used the Ionization Energy of the ground state of electron(13.6 eV), and used the following approach:
13.6eV=kT, where k=8.62e-5eV/K.
I got that part right, so I figured that I could use the Ionization energy of deuterium (14.9eV) for the 2nd part, but this doesn't give me the right answer. Does anyone know why this is so and if there's another approach to the problem?
 
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  • #2
Dissociating the deuteron is not splitting an electron from a deuterium nucleus, it's splitting the proton from the neutron in the deuterium nucleus. That's an energy that should be measured in MeV, not eV. Where did you get 14.9eV??
 
  • #3
I got it somewhere online, and it didn't seem right. I can't think of any other way of going about the problem though, and I can't find any other value for that ionization energy.
 
  • #4
The relevant energy is the binding energy of the proton and neutron that form the deuteron, not the binding energy of the electron in a deuterium atom.
 
  • #5
What's the mass difference between a free proton and neutron and the deuterium bound state? Times c^2. That's that's the 'ionization' energy you are looking for.
 
  • #6
Ok, so calculating that would give me 1875.6 MeV for he 'ionization energy' of the deuteron. Then, when I set it equal to kT, I get 2.177e13K, which still isn't the right answer. Am I on the right track at least?
 
  • #7
freefallin38 said:
Ok, so calculating that would give me 1875.6 MeV for he 'ionization energy' of the deuteron. Then, when I set it equal to kT, I get 2.177e13K, which still isn't the right answer. Am I on the right track at least?

That number is really way wrong. That's about the total mass of deuterium.
 
  • #8
ohh ok, i got it now. i just had some trouble with using the right masses haha. thank you so much!
 

1. What is the "Temp. of Universe hw problem"?

The "Temp. of Universe hw problem" refers to a homework problem or exercise that focuses on calculating the temperature of the universe at a given point in time. It is often used to help students understand concepts related to the Big Bang theory and the early stages of the universe.

2. How is the temperature of the universe calculated?

The temperature of the universe can be calculated using the Planck equation, which relates the energy of a photon to its frequency. This equation can be used to determine the temperature of the cosmic microwave background radiation, which is a remnant of the Big Bang and is believed to be the most accurate representation of the universe's temperature.

3. Why is the temperature of the universe important?

Calculating the temperature of the universe can provide valuable insights into the early stages of our universe and its evolution. It can also help us understand the formation and distribution of galaxies, as well as the composition of the universe.

4. How has the temperature of the universe changed over time?

The temperature of the universe has decreased as the universe has expanded. According to the Big Bang theory, the universe started out extremely hot and dense, but as it expanded, it cooled down. Currently, the estimated temperature of the universe is approximately 2.73 Kelvin (-270.42 degrees Celsius or -454.76 degrees Fahrenheit).

5. Can the temperature of the universe ever reach absolute zero?

No, the temperature of the universe cannot reach absolute zero. This is because absolute zero is defined as the point where all molecular motion ceases, and the universe will always have some level of energy and motion. However, the temperature of the universe is expected to continue dropping as it expands further.

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