Discussion
At what temperature, the population in v = 1 level of I2 would become half the population in ground energy level ? (Given : \(\dfrac{hc\bar{v}}{k}\) = 346.5 K)
Answer: B
The temperature is 500 K.
For the vibrational levels (each non-degenerate) the Boltzmann ratio is set by the energy gap hcν̄ between v = 1 and v = 0:
\[ \frac{N_{1}}{N_{0}} = e^{-hc\bar{\nu}/kT} = \frac{1}{2} \]
\[ \begin{aligned} \frac{346.5}{T} &= \ln 2 = 0.693 \\ T &= \frac{346.5}{0.693} = 500\ \text{K} \end{aligned} \]
773 K and 227 K are 500 K with 273 added or subtracted, a slip between kelvin and degrees Celsius, and 300 K is simply room temperature.
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