(a) 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. What is the rms speed of the deuterons? Is this a significant fraction of the speed of light in vacuum (c = 3.0 X 108 m/s)? (b) What would the temperature of the plasma be if the deuterons had an rms speed equal to 0.10 c?
Solution 35E Step 1: Given data: 27 Deuteron mass: m = m + p = 3n348 × 10 kg Temperature T = 300 × 10 K 6 Step-2: (a).The root mean square velocity of a molecule is V rms = 3k T/m B 23 6 27 V rms = 3(1.3806 × 10 )(300 × 10 )/(3.348 × 10 ) V = 1.9264 × 10 m/s rms significant fraction of the speed of light in vacuum (c = 3.0 X 108 m/s) V rms/c = 0.64% very small fraction. Step-3: (b).The temperature of the plasma be if the deuterons had an rms speed equal to 0.10 c is V rms= 3k TBm Square on both sides and rearrange the equations T = mV 2/3k rms B 27 6 2 23 T = (3.348 × 10 )(1.9624 × 10 ) /3(1.3806 × 10 ) 10 T = 7.3 × 10 K
