Formulas n in n. n! r(v)=(- 1)! = e-"x-da, where v > 0. sin(k)ek dk 0. yk2 -yk2 consider n impurity atoms. each impurity can be in one of two states, with respectively. the microstates are specified by the set of occupations energies 0 and e, numbers n; }, where n; = 0 or 1 and i= . the total energy of the system is e en1 where n1 is the total number of the excited impurities. (a) in the micro-canonical ensemble: i. find the number of distinct microstates (e en1, n) ii. find the entropy s(e, n) iii. find the internal energy e(t, n) in the limit of n1, n> 1. as a function of t and n. (b) in the canonical ensemble: i. find the canonical partition function. ii. find the internal energy e (t, n).

Astudent is performing an experiment comparing sound and light waves. the student gathers the following data. what conclusion does the student most likely make based on this data? light waves always travel the same speed; however, the speed of sound is determined by the medium that it travels through. all sound waves always have the same energy, so the temperature of the medium does not affect wave speed. light needs to vibrate particles, so it travels fastest in tightly packed solids, while sound does not need a medium, so it travels fastest in a gas. tightly packed particles in solids slow down the light waves; however, sound waves make particles bounce into each other, so they travel faster in solids.

While standing outdoors one evening, you are exposed to the following four types of electromagnetic radiation: yellow light from a sodium street lamp, radio waves from an am radio station, radio waves from an fm radio station, and microwaves from an antenna of a communications system. rank these type of waves in terms of increasing photon energy.

Alandscaper is shopping for landscaping materials. she wants to use materials through which water flows easily. which materials should she choose? check all that apply. clay gravel granite rocks with cracks loosely packed soil