Periodic boundary conditions lead to a restriction of the possible k values of atomic vibrational states. consider a linear chain of copper atoms. the length of the chain is 1 cm, the lattice spacing is 0.36 nm and the force constant 50 nm calculate the smallest possible finite wave number k. what would be the vibrational angular frequency for this wave number? demonstrate that there is a standing wave at the brillouin zone boundary for the case of waves on such a row of masses. note the dispersion relation for a 1-dimensional chain is given by 141 13] 13] 4,01 . ka where co is the vibrational angular frequency, β is the force constant, a is the lattice spacing, m is the mass of a copper atom and k is the wave number. the atomic mass of copper 63.55 amu).

Consider a hydrogen atom in the ground state. what is the energy of its electron? =e= jj now consider an excited‑state hydrogen atom. what is the energy of the electron in the =5n=5 level? =e5= j

Which best describes the first law of thermodynamics as compared to the second law of thermodynamics? a. the first law describes how thermal energy is conserved but not the direction it moves. b. the first law describes the direction thermal energy moves but not how it is conserved. c. the first law describes how thermal energy can be created but not how it can be destroyed. d. the first law describes how thermal energy can be destroyed but not how it can be created.

1. what is the relationship between wavelength and the penetrating power of an electromagnetic wave? a) the penetrating power has no relationship to the wavelength. b) the penetrating power increases as the wavelength increases. c) the penetrating power decreases as the wavelength increases. d) the penetrating power decreases as the wavelength decreases. 2. as ice melts and turns into water, the speed of sound through the material would most likely do what? justify your answer. a) the speed would not change because the material is always water. b) the speed of sound would increase because the density of water is less than that of ice. c) the speed of sound would increase because energy is added to ice in order to make it melt. d) the speed of sound would decrease because sound travels faster through solids than liquids. 3.which of these waves need a medium to travel through? a) sound b) x-rays c) infrared rays d) visible light