Chem 402- Midterm Exam Guide - Comprehensive Notes for the exam ( 157 pages long!)

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, thus the probability of being in state j is: since the sum of probabilities for all the states must equal one (cid:3036)(cid:3037)= (cid:3284)(cid:3038) = 0 and all other state energies >> kt (q 1) (cid:4666) (cid:3116)(cid:3286)+ (cid:3117)(cid:3286)+ (cid:4667) (cid:3116)(cid:3286) (cid:3116)(cid:3286)=(cid:883) (probability of finding something in the ground: (cid:1842)(cid:2868), since kt becomes tiny and (cid:2868) gets bigger, the exponent on e becomes a large negative number, like 1/e(big number! If the particles are all identical, then there are indistinguishable states, and only distinguishable states count in the canonical function q. Number of distinguishable states is less if the particles are: stirling"s approximation indistinguishable must divide by n! N for distinguishable particles: qtrans = qtrans. N/n! for indistinguishable particles: ! , and thus n! = enlnne-n = nne-n: for the above example: (cid:1843)(cid:3047)(cid:3045)(cid:3046)=(cid:3044)(cid:3295)(cid:3293)(cid:3294)! It is possible to describe every single possible configuration (both energy and location) a system can exist in.

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