CHEM2912 Lecture 2: CHEM2912 Lecture 2
5 Jul 2018
School
Department
Course
Professor
CHEM2912
Chemical structure & Stability
Monica Zanuttini !
460381099
Lecture 2 Microstates and configurations
Microstates is an indicator of how probable these states are to occur. !
Assumption: Every microstate that satisfies the given N and E occurs with equal probability on the
microstate level. !
Each microstate is one possible outcome when a system distributes available energy amount
available molecules. !
!
Predicting the probability of a configuration: !
“The most probable configuration” = the equilibrium configuration. !
This is because it will become so dominant at large system sizes, everything else is unlikely to
happen. Probability approaches, but doesn't reach, one. !
Finding the most probable configuration: !
We denote the occupation numbers for this configuration by: !
!
Q: What are the values of ni* that maximise W for a given N and E?!
A: !
This formula says that the occupation number of the most probable configuration decreases
exponentially with increasing energy above the ground state. !
This contains two unknowns ß & n0*. !
ß causes the decay of how the higher energy levels are to be occupied. !
As E increases, ß decreases. !
When ß is small, exponential hasn’t decayed much, higher energy levels are occupied. !
When ß is large, exponential is very large, lowest energy levels will be occupied.!
Q: If the energy in a system is increased, there will come a point at which there are more particles
in energy level i=1 than in i=0. !
A: False. If ß goes really small (towards zero), the exponential will be very close to 1 (just below).
Occupation number of level 1 is nearly that of level 0. The ground state is always the most highly
occupied state. !
Document Summary
Microstates is an indicator of how probable these states are to occur. Assumption: every microstate that satis es the given n and e occurs with equal probability on the microstate level. Each microstate is one possible outcome when a system distributes available energy amount available molecules. The most probable con guration = the equilibrium con guration. This is because it will become so dominant at large system sizes, everything else is unlikely to happen. We denote the occupation numbers for this con guration by: This formula says that the occupation number of the most probable con guration decreases exponentially with increasing energy above the ground state. Causes the decay of how the higher energy levels are to be occupied. When is small, exponential hasn"t decayed much, higher energy levels are occupied. When is large, exponential is very large, lowest energy levels will be occupied.
