How Is Deuteron Kinetic Energy Related to Plasma Temperature in Nuclear Fusion?

[jensgt]

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 3.01×108 . What is the rms speed of the deuterons?

What would the temperature of the plasma be if the deuterons had an rms speed equal to 9.0×10−2 ?

Homework Equations

Vrms = √(3KT/m)

1/2mv² = 3/2KT

mVrms²/(3K) = T

The Attempt at a Solution

I went over this about 100 times before giving up. The answer I know is 5.9x10¹⁰K but even with that I can't get the answer. It is driving me sort of crazy so I figured I would ask if someone could help. The K I am using is 1.38x10^-23J/K and the m is 3.34x10^-27kg

help!

 

[ehild]

Use units, please. In what unit the rms speed has to be 9.0×10⁻² and temperature 3.01×10⁸?

ehild

 

[jensgt]

Speed = m/s and temp = K

 

[ehild]

Have you copied the rms speed correctly? 9.0x10^-2 m/s is unrealistic. Even at room temperature, the rms speed is about 2000 m/s for the deuteron.

ehild