For which of the following molecule is the high temperature expression...
Explanation:
To determine which molecule the high temperature expression for the rotational partition function is valid for, we need to consider the value of the rotational constant (B) for each molecule and compare it to the temperature (T) given.
The high temperature expression for the rotational partition function is given by:
Q_rot = T / B
If T is much greater than B, then the high temperature expression is valid.
Let's analyze each molecule:
a) DBr (B = 4.24 cm-1)
b) DI (B = 3.25 cm-1)
c) CsI (B = 0.0236 cm-1)
d) F35CI (B = 0.516 cm-1)
Comparing T = 40 K to the rotational constant for each molecule:
a) DBr (T/B = 40 K / 4.24 cm-1 = 9.43 K/cm-1)
b) DI (T/B = 40 K / 3.25 cm-1 = 12.31 K/cm-1)
c) CsI (T/B = 40 K / 0.0236 cm-1 = 1694.92 K/cm-1)
d) F35CI (T/B = 40 K / 0.516 cm-1 = 77.52 K/cm-1)
Comparing T to B:
From the calculations above, we can see that for CsI, T/B is the largest value (1694.92 K/cm-1) compared to the other molecules. This indicates that T is much greater than B for CsI, suggesting that the high temperature expression for the rotational partition function is valid for this molecule.
Conclusion:
The high temperature expression for the rotational partition function is valid for CsI (Cesium Iodide) when T = 40 K.