The temperature at which protons in proton gas would have enough energy to overcome. Coulomb barrier of $4.14 imes 10^{- 14}J$ is (Boltzman constant $= 1.38 imes 10^{- 23}JK^{- 1}$)

Question

The temperature at which protons in proton gas would have enough energy to overcome. Coulomb barrier of $4.14 	imes 10^{- 14}J$ is (Boltzman constant $= 1.38 	imes 10^{- 23}JK^{- 1}$)

Dr. Abubacker · Accepted Answer

(a) The temperature at which protons in a proton gas would have enough energy to overcome Coulomb barrier between them is given by
$\frac{3}{2}k_{B}T = K_{av}$ …(i)
Where $k_{av}$ is the average kinetic energy of the proton, $T$ is the temperature of the proton gas and $k_{B}$ is the Boltzmann constant
From (i), we get $T = \frac{2K_{av}}{3K_{B}}$
Substituting the values, we get
$T = \frac{2 	imes 4.14 	imes 10^{- 14}J}{3 	imes 1.38 	imes 10^{- 23}JK^{- 1}} = 2 	imes 10^{9}K$

Q. The temperature at which protons in proton gas would have enough energy to overcome. Coulomb barrier of $4.14 \times 10^{- 14}J$ is (Boltzman constant $= 1.38 \times 10^{- 23}JK^{- 1}$)

Explanation

Reviewed by Dr. Abubacker

Want more practice?