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 × 10-23J/k)

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 × 10-23J/k) (A) 3770 K (B) 7370 K (C) 7730 K (D) 7330 K

Tardigrade Admin · Accepted Answer

Given, K =1.38 ×-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 ⇒ 1 × 1.6 × 10-19=1.5 × kT ⇒ T =(1.6 × 10-19/1.5 × 1.38 × 10-23)=7730 K

Q. 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=1.38×10−23J/k)

3770 K

7370 K

7730 K

7330 K

Given, K=1.38×−23J/K Potential difference V=1 volt So, the average translational energy is given by the equipartition theorem, E=1.5kT where E=1eV ⇒1×1.6×10−19=1.5×kT ⇒T=1.5×1.38×10−231.6×10−19​=7730K

Q. 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 ? $(k = 1.38 \times 1 0^{- 23} J / k)$