The average kinetic energy per molecule of helium gas at temperature T is E and the molar gas constant is R. Then Avogadro's number is equal to :

\(\frac{3RT}{2E}\)

Average kinetic energy per unit molecule : E = \(\frac{3}{2}kT\)

\(k = \frac{2E}{3T}\)

But, avogadro's Number = N_A = \(\frac{R}{k} = \frac{R}{2E/3T}\)

N_A = \(\frac{3RT}{2E}\)