Statistical Mechanics A new molecule, substance X, is discovered. X is best serv

Question

Statistical Mechanics A new molecule, substance X, is discovered. X is best served chilled because the molecule has a stable state (prevalent at low temperatures and an unstable state (prevalent at high temperatures), which forms a contact explosive in bulk form. A large sample of X is prepared. At room temperature (i.e., 300 K), exactly 2/3 of the X molecules are in the lower energy (stable) state, whereas 1/3 are in the higher energy (unstable) configuration. Assuming a degeneracy factor of 1 for both the lower and higher energy states, what is the energy difference (in electron volts) between the stable and the unstable forms of molecule X?

Explanation / Answer

Solution :-

Given

A new molecule substance X is discovered. X is best served chilled because the molecule has a stable state (present at low-temperature) and an unstable state ( prevalent at high temperatue), which forms a contact explosive in bulk form.

A large sample X is prepared. At room temperature (i.e. 300 K) exactly 2/3 of X molecules are in lower energy state i.e. stable state whereas 1/3 are in the higher energy i.e.unstable configuration.

Let us assume degeneracy factor of 1 for both the lower and higher energy states.,

Energy differency in electron volts between stable and unstable form of molecules X = 2X/3 - 1/3 x (1.6 *10-19)

= X/3 * 1.6 *10^-19

= X/3 ev

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