Question

1. Diatomic nitrogen's oscillation frequency is about 6.2 x 10¹³ Hz. What is the spacing between excited vibration energy states of nitrogen? Give your answer in eV.

1a. What is the zero-point energy of the vibration mode of diatomic nitrogen if its oscillation frequency is 6.2 x 10¹³ Hz? Give your answer in eV.

1c. Per the equipartition theorem in thermodynamics, each degree of freedom of a system has (on average) of energy. Vibration modes of molecules like nitrogen do not share this degree of freedom until the available thermal energy can excite molecules into the first excited state (above the zero-point energy). At what temperature would correspond to this energy? Give your answer in Kelvin. Assume the vibration mode frequency is 6.2 x 10¹³ Hz.

Answer 1

Answers :-

Part a)0.2567 eV

Part b) 0.1283 eV

Part c) 992.2 K

For Nitrogen ,degree of freedom is 6:- Translational-3, Rotational-2,Thermal-1 .