EXERSICE 1 Calculate: a) the thermal De Broglie wavelength and b) the transport contribution to the sum of states of a Xe atom inside a cubic container of side 2.00 cm at a temperature of 4000 K Data: AB(Xe) = 131.29 amu
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- Describe the physical origins of linewidths in the absorption and emission spectra of gases. liqu ids. and solids. How may they be reduced?Calculate the relative populations of two quantum statesseparated by an energy of 0.4 × 10-21 J if the temperatureis 25°C.A 1.00 kg weight is traveling at a constant velocity of 10.0 ms-1, in a cubic room 3.00 m on an edge.(a). Determine the sum of the squares of its three quantum numbers.(b). What would be the ground state energy for this weight?
- What are differences between n→π* and π →π* bonding electron transition in Fluorescence? Please answer shorty at your own words. Answer should be to the point.Discuss qualitatively how you would expect the exciton binding energy in a GaAs/Alo.3Gao.7As quantum well to vary with the quantum well thickness, given that the binding energy of the excitons in bulk GaAs and Alo.3Gao.7As are 4 meV and 6 meV respectively.(a) Show that all reciprocal lattice vectors of the form G= hA+ kB+IC are perpendicular to the planes of the same indices (h, k, l) in real space.
- (b) A system with chemical potential u = 12.5 meV contains identical particles each with integer spin and has a single quantum state at energy E, = 0 meV. The temperature of the system is fixed at 290 K. To three significant figures, what is the ratio Pg/P1, where P is the probability of finding a single particle in the state Eo, and P3 is the probability of finding 3 particles in this state? P3/P (Input your answer as a number.)Use eqn 14D.4 to deduce expressions for (a) the root-mean-square separation of the ends of the chain, (b) the mean separation of the ends, and (c) their most probable separation. Evaluate these three quantities for a fully flexible chain with N = 4000 and l = 154 pm.The moment of inertial of 12 C-16 O is I = 1.454 × 10°46 kg*m². The molecule also has a force constant for the C-O bond of 1920N*m. Take the atomic masses of 12 C to be 12.00aμ and 160 to be 16.00aµμ and the conversion factor from 16 atomic mass unit to kg to be 1, 66054 x 1027 kμ. a) Calculate the bond length for the 12 C-1 O molecule b) Calculate a the reduced mass for the 12 C-16 O molecule c) Calculate the vibrational frequency of 12 C-160 d) Calculate the zero point vibrational energy of this molecule e) Calculate the moment of inertia for the molecule f) Calculate the rotational energy of the J = 1 and J = 2 energy levels
- Suppose an oxygen atom (m = 15.9949mu) is adsorbed on the surface of a nickel nanoparticle by a bond of force constant 544 N m-1. Calculate the wavelength of a photon needed to excite a transition between its neighbouring vibrational energy levels.The rotational constant of 127I35CI is 3.423 GHz. Ca lculate the ICI bond length.Given these two equations, calculate Cv for CO2 and N2 using the velocity of sound. 6. According to statistical mechanics, the contribution to Cy due to the ith vibrational mode of a molecule is c ee;/T Cv,vib,4 = R(7) ³ (e®,/T — 1)² › where Oi = hcv./kB, h is Planck's constant, and c is the speed of light in cm s-¹. v; is the vibrational frequency of the ith vibrational mode in wavenumbers (cm-¹). The quantity O, has dimensions of temperature and is sometimes referred to as the vibrational tem- perature (of the ith vibrational mode). The total vibrational contribution to the molar heat capacity for an N-atom (linear) molecule is then Cy,vib Cv,vib,i Calculate Cy for CO₂ at 300 K, assuming that the translational and rotational con- tributions are (3/2)R and R, respectively, and use the preceding equations to obtain the vibrational contribution. Four vibrational modes for CO₂ are expected (3N- 5). How- ever, three fundamental frequencies are observed at v= 667.3, 1340, and 2349.3 cm-¹.…