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 (duetorium) hydrogen, we can use the relationship between average kinetic energy and temperature.
The average kinetic energy of a particle (in this case, a hydrogen nucleus) can be related to the temperature using the equipartition theorem, which states that each degree of freedom of a particle contributes (1/2)kT to its average kinetic energy. In this case, a hydrogen nucleus has three degrees of freedom (since it moves in three dimensions), so its average kinetic energy can be expressed as:
Average Kinetic Energy = (3/2)kT
Given that the average kinetic energy required for nuclear fusion is at least 0.72 MeV (mega electron volts), we can convert it to joules using the conversion 1 MeV = 1.6 x 10^-13 joules. Therefore:
Average Kinetic Energy = 0.72 MeV
= 0.72 x 1.6 x 10^-13 joules
Now we can equate this to the equation for average kinetic energy:
(3/2)kT = 0.72 x 1.6 x 10^-13
Substituting the value of the Boltzmann constant (k = 1.38 x 10^23 J/K), we can solve for T, the temperature:
(3/2) x 1.38 x 10^23 x T = 0.72 x 1.6 x 10^-13
T = (0.72 x 1.6 x 10^-13) / ((3/2) x 1.38 x 10^23)
By solving the above equation, the resulting value of T will give us the required temperature for nuclear fusion to occur with deuterium hydrogen.
Please note that the calculation provided is an example of how to approach the problem. The actual calculation may involve more precise values and additional considerations.