An experiment determines that there are 49 allowed rotational energies for a diatomic molecule whose moment of inertia is 2 *0 10-46 kg .m2.The maximum rotational kinetic energy (in eV) is:
A)0.6
B)0.2
C)0.4
D)0.8
E)1.0

Question

Quizplus · Accepted Answer

The maximum rotational kinetic energy of a diatomic molecule can be calculated using the formula:

$E_{rot,max}=\frac{hcB}{4}$

where $h$ is Planck's constant, $c$ is the speed of light, and $B$ is the rotational constant, given by:

$B=\frac{\hbar^2}{2I}$

where $\hbar$ is the reduced Planck's constant and $I$ is the moment of inertia.

Substituting the given values, we get:

$B=\frac{\hbar^2}{2I}=\frac{(1.0546	imes10^{-34}/2\pi)^2}{2	imes2	imes10^{-47}}=1.383	imes10^{-23}	ext{ J}$

$E_{rot,max}=\frac{hcB}{4}=\frac{(6.626	imes10^{-34})(2.998	imes10^8)(1.383	imes10^{-23})}{4}=0.408	ext{ eV}$

Therefore, the closest option is (C) 0.4.

An Experiment Determines That There Are 49 Allowed Rotational Energies