Question

1. 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 3.10×10⁸ K . What is the rms speed of the deuterons?

2. Is this a significant fraction of the speed of light ( c = 3.0×108m/s )?

3. What would the temperature of the plasma be if the deuterons had an rms speed equal to 7.0×10⁻²c?

Answer 1

Solution::

(A)

We know that rms speed is given by

Vrms=sqrt(3KT/m)

Where k is boltzman constant = 1.38*10-23
T is temperature = 3.1*108 K
m is mass = 2*(1.67*10-27) kg

Vrms=sqrt((3*1.38*10^-23*3.1*10^8)/(2*1.67*10^-27))

Vrms = 1.96*106 m/s
(B) now
fraction = Vrms/C

= 1.96*106/3*108

= 6.53*10-3
Therefore the value is very small and fraction is insignificant.
(C) if Vrms = 7*10-2C

= 7*10-2*3*108

= 21*106 m/s

21*10^6=sqrt((3*1.38*10^-23*T)/(2*1.67*10^-27))

On solving it we get
T = 3.56*1010 K