please answer 3.) The lowest two electronic energy levels of the molecule NO are two-fold degenerate...
hc 3 (25pt) Consider a set of n energy levels that are evenly-spaced by energy and that each level is n-fold degenerate. The degeneracy of the energy levels allows us to write the molecular partition function as: a. Approximate this sum by an integral and find an analytical form of the partition function. b. Calculate the partition function at 298 K given that A -100 microns. c. Find the contribution to internal energy from statistical mechanical expression,
hc 3 (25pt)...
A system consists of two non-degenerate states separated in energy by an amount e As the temperature is raised towards infinity, which of the following statements is correct? A. The frequency of photons whose energy matches the transition energy goes do B. The population in the upper state will exceed that in the ground state. C. The probability of a molecule occupying either state becomes similar D. At a sufficiently high temperature laser action will occur. Ground state Br2 dissociates...
(7) Relative population of two energy (atomic or molecular) levels is given by Boltzmann distribution law which is mathematically represented as: kgT Here Ni, N, represent number of atoms/molecules in ith and jth energy levels, respectively; g. g represent degeneracy ofith and jth energy levels, respectively; E E; represent energies ofi and jt levels, repsectively represents Boltzmann constant and T represents temperature in kelvin. For non-degenerate states g = 1· (a) Find the population ratio between n-2 and n-1 levels...
Question 5 The rotational energy levels of a diatomic molecule are given by E,= BJ(J+1) with B the rotational constant equal to 8.02 cm Each level is (2) +1)-times degenerate. (wavenumber units) in the present case (a) Calculate the energy (in wavenumber units) and the statistical weight (degeneracy) of the levels with J =0,1,2. Sketch your results on an energy level diagram. (4 marks) (b) The characteristic rotational temperature is defined as where k, is the Boltzmann constant. Calculate the...
Question 3 a) Consider the hypothetical case of two degenerate quantum levels of energy E1, E2 (E. < Ez) and statistical weights g1 = 4, 92 = 2. These levels have respective populations N1 = 3 and N2 = 1 particles. What are the possible microstates if the particles are (1) bosons (6 marks) or (ii) fermions (6 marks)? AP3, PHA3, PBM3 PS302 Semester One 2011 Repeat page 2 of 5 b) Show how the number of microstates would be...
Consider an element with energy levels ?0E0 and ?∗E∗and degeneracies of those energy levels ?0g0 and ?∗,g∗, respectively. Determine the fraction of atoms of the element in the excited state (?∗/?0)(N∗/N0) at 6995 K6995 K if the wavelength difference of the two states is 440.5 nm,440.5 nm, and ?0=1g0=1 and ?∗=3.
11-4 Five indistinguishable particles are to be distributed among the four equally spaced energy levels shown in Fig. -2 with no restriction on the number of particles in each energy state. If the total energy is to be 1261. (a) specify the occupation number of each level for each macrostate, and (b) find the number of microstates for each macrostate, given the energy states represented in Fig. 11-2. 11-5 (a) Find the number of macrostates for an assembly of four...
Calculate the entropy for a system consisting of 10 particles distributed over four energy levels with occupancies of (5, 3, 2, 0) 1. 2. If there exists two excited states at energies of 0.72 and 1.24 kJ mol above the ground state of a system, 0 kJ mol. What would be the percentage of particles occupying each state at equilibrium when the temperature is 300 K 3. Evaluate q for a nitrogen molecule (molecular weight 28.0134 g mol) at 25...
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(2) The simplified electronic/vibrational/rotational energy level diagram for a molecule (called a Jablonski diagram) is shown below. Transitions involving photons are shown with wavy arrows. Arrow (a) represents 319 kJ mol-1. In this simplified example the energy levels in the singlet states and triplet states are equally spaced but in a real molecule they become closer together at higher energy. Use this diagram for questions 2-5. Energy So de...
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The force constant for the carbon monoxide molecule is 1,908 N m At 1,000 K what is the probability that the molecule will be found in the lowest excited state? At a given temperature the rotational states of molecules are distributed according to the Boltzmann distribution. Of the hydrogen molecules in the ground state estimate the ratio of the number in the ground rotational state to the number in the first excited...