Rotational energy levels for diatomic molecules

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Presentation transcript:

Rotational energy levels for diatomic molecules l = 0, 1, 2... is angular momentum quantum number I = moment of inertia CO2 I2 HI HCl H2 qR(K) 0.56 0.053 9.4 15.3 88

Vibrational energy levels for diatomic molecules n = 0, 1, 2... (harmonic quantum number) w w = natural frequency of vibration I2 F2 HCl H2 qV(K) 309 1280 4300 6330

Specific heat at constant pressure for H2 CP = CV + nR H2 boils w CP (J.mol-1.K-1) Translation

More on the equipartition theorem Classical uncertainty: Where is the particle? V(x) V = ∞ V = ∞ V = 0 W = 9 x x = L

More on the equipartition theorem Classical uncertainty: Where is the particle? V(x) V = ∞ V = ∞ V = 0 W = 18 x x = L

More on the equipartition theorem Classical uncertainty: Where is the particle? V(x) V = ∞ V = ∞ V = 0 W = 36 x x = L

More on the equipartition theorem Classical uncertainty: Where is the particle? V(x) V = ∞ V = ∞ V = 0 W = ∞ S = ∞ x x = L

More on the equipartition theorem: phase space Area h Cell: (x,px) dpx px dx x

More on the equipartition theorem: phase space Area h Cell: (x,px) dpx px dx x

More on the equipartition theorem: phase space Area h Cell: (x,px) dpx px dx x

More on the equipartition theorem: phase space In 3D: Uncertainty relation: dxdpx = h dpx dx

Examples of degrees of freedom: