Question

A deuteron, 21H, 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 2.94×10^8 K . What is the rms speed of the deuterons?

Answer 1

Answer:

1917723.40119 m/s

Explanation:

m = Mass of deuteron = $(1.637+1.675)\times 10^{-27}=3.312\times 10^{-27}$

k = Boltzmann constant = $1.381\times 10^{-23}\ J/K$

T = Temperature = $2.94\times 10^8\ K$

RMS velocity is given by

$V_r=\sqrt{\dfrac{3kT}{m}}\\\Rightarrow V_r=\sqrt{\dfrac{3\times 1.381\times 10^{-23}\times 2.94\times 10^8}{3.312\times 10^{-27}}}\\\Rightarrow V_r=1917723.40119\ m/s$

The RMS velocity of the deutrons is 1917723.40119 m/s