What Is the RMS Speed of Deuterons in a Fusion Reactor?

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SUMMARY

The discussion centers on calculating the root mean square (RMS) speed of deuterons in a fusion reactor, specifically at a temperature of 300 million K. The formula used is vrms = √(3RT/M), where R is the gas constant (8.314 J/(mol·K)) and M is the molar mass of deuterons. Participants clarified that the molar mass M should be calculated as the sum of the masses of one proton and one neutron, approximately 2.014 g/mol, which is essential for accurate RMS speed calculations. The RMS speed at this temperature is a significant fraction of the speed of light, approximately 0.1c.

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  • Knowledge of molar mass calculations
  • Basic physics concepts related to speed and temperature
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  • Learn about the behavior of plasma at high temperatures
  • Explore the significance of deuterium in fusion reactions
  • Study the relationship between temperature and particle speed in thermodynamics
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Homework Statement



A deuteron is the nucleus of a hydrogen isotope and consists of one proton and one neutron. The
plasma of deuterons in a nuclear fusion reactor must be heated to about 300 million K.
(a) What is the RMS speed of the deuterons? Is this a significant fraction of the speed of light c =
3 x 10^8 m/s?
(b) What would the temperature of the plasma be if the deuterons had an RMS speed equal to
0.10 c?

R=8.314; T=300E6K

Homework Equations



v_{rms}=\sqrt{\frac{3RT}{M}}

The Attempt at a Solution



I know how to solve this, but I don't get the first part of the question. how do you find M? I tried M=1.008, but that doesn't make sense.
 
Last edited:
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If a deuteron has one proton and one neutron, does it make sense that M = 1.008?

After all, you can look these things up on the internet.
 
oh, thanks. I just add Mp + Mn to get M...right?
 

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