For instance. four molecules in a three-level system: the following two conformations have the same probability 画mm 2 l--2 8 8 ======= a demon
For instance, four molecules in a three-level system: the following two conformations have the same probability. ---------l-l-------- 2 ---------l--------- 2 ---------l---------- ---------1-1-1---- ---------l---------- 0 ------------------- 0 a demon
THE DISTRIBUTION OF MOLECULAR STATES Consider a system composed of n molecules and its total energy e is a constant. These molecules are independent, i. e no interactions exist among the molecules
THE DISTRIBUTION OF MOLECULAR STATES Consider a system composed of N molecules, and its total energy E is a constant. These molecules are independent, i.e. no interactions exist among the molecules
Population of a state: the average number of molecules occupying a state. Denote the energy of the state 8 The Question: How to determine the population
Population of a state: the average number of molecules occupying a state. Denote the energy of the state i The Question: How to determine the Population ?
Configurations and Weights Imagine that there are total N molecules among which no molecules with energy co, n, with energy 81) n, with energy a,, and so on, where 8o <8,<8,<... are the energies of different states. The specific distribution of molecules is called configuration of the system, denoted as i no, nis
Configurations and Weights Imagine that there are total N molecules among which n0 molecules with energy 0 , n1 with energy 1 , n2 with energy 2 , and so on, where 0 < 1 < 2 < .... are the energies of different states. The specific distribution of molecules is called configuration of the system, denoted as { n0 , n1 , n2 , ......}
N,D,0,……} corresponds that every molecule is in the ground state, there is only one way to achieve this configuration; N-2, 2, 0,.o.3 corresponds that two molecule is in the first excited state and the rest in the ground state and can be achieved in N(N-1)/2 ways A configuration (no, nu, n 2,…… can be achieved in w different ways, where w is called the weight of the configuration And w can be evaluated as follows W=M!/(mnln1n2…)
{N, 0, 0, ......} corresponds that every molecule is in the ground state, there is only one way to achieve this configuration; {N-2, 2, 0, ......} corresponds that two molecule is in the first excited state, and the rest in the ground state, and can be achieved in N(N-1)/2 ways. A configuration { n0 , n1 , n2 , ......} can be achieved in W different ways, where W is called the weight of the configuration. And W can be evaluated as follows, W = N! / (n0 ! n1 ! n2 ! ...)