If the average translational kinetic energy of air molecules is given as 0.040 eV ( 1 eV = 1.6 10⁻¹⁹ J ), determine the temperature of the air. Take the Boltzmann constant to be k = 1.38 10⁻²³ J K ⁻¹ .

Step-by-step solution

The average translational kinetic energy of a gas molecule is given by E = 3 2 kT . Given E = 0.040 eV = 0.040 1.6 10⁻¹⁹ J = 6.4 10⁻²¹ J . Substituting the values into the formula: 6.4 10⁻²¹ = 3 2 1.38 10⁻²³ T T = 2 6.4 10⁻²¹ 3 1.38 10⁻²³ T = 12.8 100 4.14 309.18 K The closest value among the options is 310 K .