Question

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

• A. $ 2\times {{10}^{9}}K $
• B. $ {{10}^{9}}K $
• C. $ 6\times {{10}^{9}}K $
• D. $ 3\times {{10}^{9}}K $
• E. $ 4.5\times {{10}^{9}}K $

Answer 1

Answer: (A)

Given: $ k=1.38\times {{10}^{-23}}J{{K}^{-1}} $
The energy of proton gas
$ =4.14\times {{10}^{-14}}J $
$ \therefore $ $ E=\frac{3}{2}kT $
or $ 4.14\times {{10}^{-14}}=\frac{3}{2}\times 1.38\times {{10}^{-23}}\times T $
$ T=2\times {{10}^{9}}K $