Calculate, by explicit summation, the vibrational partition function of I₂ molecules at (a) 100 K, (b) 298 K given that its vibrational energy levels lie at the following wavenumbers above the zero-point energy level 0, 215.30, 425.39, 636.27, 845.93 cm⁻¹. What proportion of I₂ molecules are in the ground and first two excited levels at the two temperatures?
a) 2.32, 3.12, 94.56%, 5.44%
b) 6.54, 5.32, 83.27%, 16.73%
c) 1.23, 4.56, 96.78%, 3.22%
d) 4.35, 2.12, 87.91%, 12.09%