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- A particle is confined to a two-dimensiona I ring of radius 100 pm. What are the wavelengths of the wavefunctions of the t hree lowest rotational levels?There are two copper wires placed side by side separated by a Cuo insulator. By modeling the insulator as a barrier potential with a height of 15.0 eV, calculate the transmission and reflection coefficients for electrons with an energy of 10.00 eV if the insulator thick is 10.00 nm.(a) Write the expression of average no. of particle (s) in particular single particle quantum state (s) for a quantum gas of N identical particle at temp. T. If partilcle is fermion then show that- Here B - ns = 1 kT 1 ea+Bei +1 energy of state.
- Using the derived partition function for a single harmonic oscillator in three different directions provided above, show that the partition function for a crystal of n atoms is given byA beam of electrons with kinetic energy 350 eV is incident normal to the surface of a KC1 crystal that has been cut so that the spacing d between adjacent atoms in the planes parallel to the surface is 0.315 nm. (a) There are multiple diffraction peaks from this scattering corresponding to different inte- gers n in the Bragg condition. Show that there is a maximum n above which diffraction peaks are not possible, and find this integer nmax. (b) Calculate the angles at which diffraction peaks will occur for all orders that are possible.Heat capacity and equipartition Find the classical physics prediction for the heat capacity of10 cm3of a substance which crystallises as FCC and has lattice constant 571 pm.
- A copper vapour laser operates at a temperature 1,.000 K. The lasing level is found in the copper atom in the gas with a spontaneous emission lifetime of 500.0 ns and a central transition wavelength of 510.6 nm. Calculate the size width of the lineshape due to the dominant broadening mechanism.Find an explicit relation for the chemical potential u of a 2DEG at a finite temperature.What is the energy separation (ΔE) between the n = 4 and n = 5 states for an F2 molecule trapped within in a one-dimension well of length 3.0 cm? At what value of n does the energy of the molecule reach ¼kBT at 450 K, and what is the separation between this energy level and the one immediately above it?
- The vibrational wavenumber of HBr is 264 cm-1 Evaluate the vibrational partition function of HBr at 298 K using both the exact and the approximate expressions.The Bragg angles (8) corresponding to the (100) and (001) planes of an hexagonal crystal, measured using Cuk, radiation (=1.542 A) were found to be 8.68° and 6.82°, respectively. Calculate the lattice parameters.if we have to generate light of (v = 4.74 10 Hz) wavelength at temperature(300K) from the system of He-Ne, Calculate the ratio of spontaneous and stimulated emission, and find the equilibrium populations of levels energy of this room transition?