Question

At what temperature does the average transnational kinetic energy of a molecule in a gas become equal to kinetic energy of an electron accelerated from rest through a potential difference of $1$ volt? ($k=1.38\times {10}^{-23}J/K)$

• A. $3770K$
• B. $7370K$
• C. $7730K$
• D. $7330K$

Answer 1

The correct option is C $7730K$

Given, $K=1.38{\times }^{-23}J/K$

Potential difference $V=1$ volt

So, the average translational energy is given by the equipartition theorem,

$E=1.5kT$

where $E=1eV$

$\Rightarrow 1\times 1.6\times {10}^{-19}=1.5\times kT$

$\Rightarrow T=\frac{1.6\times {10}^{-19}}{1.5\times 1.38\times {10}^{-23}}=7730K$