Nuclear fusion reaction will occur in a gas duetorium hydrogen nuclei when a nuclei has an average kinetic energy of atleast 0.72MeV. What is the temperature required for nuclear fusion to occur with duetorium hydrogen? (take boltmann constant k = 1.38 x 10^23 j/k)
To determine the temperature required for nuclear fusion to occur with deuterium hydrogen, we can use the concept of thermal equilibrium.
In thermal equilibrium, the average kinetic energy of particles is related to temperature. This relationship is given by the equation:
E_avg = (3/2) * k * T
Where:
E_avg is the average kinetic energy of particles
k is the Boltzmann constant (1.38 x 10^23 J/K)
T is the temperature in Kelvin
In this case, we are given that the average kinetic energy required for nuclear fusion to occur with deuterium hydrogen nuclei is at least 0.72 MeV.
To convert this energy into joules, we need to use the relationship that 1 MeV = 1.6 x 10^-13 J (since 1 electron volt is equal to 1.6 x 10^-19 J).
So, 0.72 MeV = 0.72 * 1.6 x 10^-13 J = 1.152 x 10^-13 J
Now, we can equate the given energy with the equation for average kinetic energy:
1.152 x 10^-13 J = (3/2) * (1.38 x 10^23 J/K) * T
Let's solve for T:
T = (1.152 x 10^-13 J) / ((3/2) * (1.38 x 10^23 J/K))
T = 5.56 x 10^9 K
Therefore, the temperature required for nuclear fusion to occur with deuterium hydrogen nuclei is approximately 5.56 x 10^9 Kelvin.