Question

At what temperature does the average translational 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. 3770 K
• B. 7370 K
• C. 7730 K
• D. 7330 K

Answer 1

Answer: (C)

Given, $K =1.38 \times^{-23} J / K$
Potential difference $V =1$ volt
So, the average translational energy is given by the equipartition theorem, $E =1.5 kT$
where $E =1 eV$
$\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}}=7730 K $