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For which of the following diatomic molecules is the high-temperature expression for the rotational partition function...
A. Derive an expression for the rotational partition function in the "high-temperature" limit where qrot can...
A. Derive an expression for the rotational partition function in the "high-temperature" limit where qrot can be approximated as an integral. Remember that the rotational energies as a function of rotational quantum number j are given by: ϵ (j) = B j (j + 1) where B is called the “rotational constant” B = ℏ2 /2µ r 2 , and the degeneracy of each "j" state is D(j) = 2j + 1. B. What is the average rotational energy in...
Consider rotational motion of heteronuclear diatomic molecules at a temperature T using the rigid-rotator approximation. (a)...
Consider rotational motion of heteronuclear diatomic molecules at a temperature T using the rigid-rotator approximation. (a) Write expression for the probability to find a diatomic molecule in a particular rotational level using the Boltzmann distribution. (b) Find the most populated rotational level for ^127 I ^35 Cl at 300 K.
Question 5 The rotational energy levels of a diatomic molecule are given by E,= BJ(J+1) with...
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...
At a given temperature, the difference between the specific heats of a diatomic ideal gas and...
At a given temperature, the difference between the specific heats of a diatomic ideal gas and a monatomic gas is partly due to rotational energy of the diatomic molecules. A quantum rigid rotator has energy levels Erot (1) with degeneration given by ħ2 Erot(1) = 1(1+1) g() = 21+1, 1 = 0, 1, 2,... g(0) 21 where I is the moment of inertia. (a) Find the canonical partition function of a gas of N non-interacting diatomic molecules. (b) Evaluate the...
Determine the following speeds (in m/s) for molecules of the diatomic gas hydrogen at a temperature...
Determine the following speeds (in m/s) for molecules of the diatomic gas hydrogen at a temperature of 815 K. Use 2.02 x 10-3 kg/mole as the molar mass for hydrogen molecules. (a) root mean square speed 3176 m/s (b) average speed Check your text for an expression which will allow you to determine the average speed of the gas molecules. Enter the temperature in degrees kelvin, take into consideration that we are dealing with a diatomic gas, and be sure...
a.) What does a partition function represent in statistical thermodynamics? A. The number of rotational symmetry...
a.) What does a partition function represent in statistical thermodynamics? A. The number of rotational symmetry elements of a molecule with more than 2 atoms. B. The number of thermally accessible energy levels at a given temperature. C. The number of molecules that partition themselves between the liquid and the gas phase of a substance b.) The constant volume heat capacity for a monoatomic gas is equal to: A. RT B. R C. 32 RT D. 3/2 R c.) The...
In the ro-vibrational model for spectra of diatomic molecules, the total rotational and vibrational energy for...
In the ro-vibrational model for spectra of diatomic molecules, the total rotational and vibrational energy for a given state is: Évj = ū(v + 3) + BJC +1) (Equation 1) where v is the vibrational quantum number and J is the rotational quantum number. Complete the following steps to create a model energy level diagram for a hypothetical diatomic molecule with ✓ = 2000 cm-1 and B = 1 cm-1. i) Draw a horizontal line to represent the ground vibrational...
Rotational states of a diatomic molecule can be approximated by those of a rigid rotor. The hamil...
Rotational states of a diatomic molecule can be approximated by those of a rigid rotor. The hamiltonian of a rigid rotor is given by hrotor 12/21, where L2 is the operator for square of angular momentum and I the moment of inertia. The eigenvalues and eigenfunctions of L2 are known: Lylnu =t(1+1)ay," , where m.--1, , +1 a) Calculate the canonical partition function : of a rigid rotor. Hint: Replace summation over by integral. b) What is the probability that...
please help 4.) Calculate the rotational partition function for Hy at 1000 K, where B=60.589 cm...
please help
4.) Calculate the rotational partition function for Hy at 1000 K, where B=60.589 cm 1
1. Calculate (a) the thermal wave-length (in pm) and (b) the translational partition function of H...
1. Calculate (a) the thermal wave-length (in pm) and (b) the translational partition function of H atom in a cubic box of side 1.0 cm at 300 K. (c) Can a hydrogern molecule be considered as a classical system (as a diatomic molecule in whiclh hydrogen atoms behave classically) at this temperature? Explain why.
Consider rotational motion of heteronuclear diatomic molecules at a temperature T using the rigid-rotator approximation. (a) Write expression for the probability to find a diatomic molecule in a particular rotational level using the Boltzmann distribution. (b) Find the most populated rotational level for ^127 I ^35 Cl at 300 K.
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...
At a given temperature, the difference between the specific heats of a diatomic ideal gas and a monatomic gas is partly due to rotational energy of the diatomic molecules. A quantum rigid rotator has energy levels Erot (1) with degeneration given by ħ2 Erot(1) = 1(1+1) g() = 21+1, 1 = 0, 1, 2,... g(0) 21 where I is the moment of inertia. (a) Find the canonical partition function of a gas of N non-interacting diatomic molecules. (b) Evaluate the...
Determine the following speeds (in m/s) for molecules of the diatomic gas hydrogen at a temperature of 815 K. Use 2.02 x 10-3 kg/mole as the molar mass for hydrogen molecules. (a) root mean square speed 3176 m/s (b) average speed Check your text for an expression which will allow you to determine the average speed of the gas molecules. Enter the temperature in degrees kelvin, take into consideration that we are dealing with a diatomic gas, and be sure...
a.) What does a partition function represent in statistical thermodynamics? A. The number of rotational symmetry elements of a molecule with more than 2 atoms. B. The number of thermally accessible energy levels at a given temperature. C. The number of molecules that partition themselves between the liquid and the gas phase of a substance b.) The constant volume heat capacity for a monoatomic gas is equal to: A. RT B. R C. 32 RT D. 3/2 R c.) The...
In the ro-vibrational model for spectra of diatomic molecules, the total rotational and vibrational energy for a given state is: Évj = ū(v + 3) + BJC +1) (Equation 1) where v is the vibrational quantum number and J is the rotational quantum number. Complete the following steps to create a model energy level diagram for a hypothetical diatomic molecule with ✓ = 2000 cm-1 and B = 1 cm-1. i) Draw a horizontal line to represent the ground vibrational...
Rotational states of a diatomic molecule can be approximated by those of a rigid rotor. The hamiltonian of a rigid rotor is given by hrotor 12/21, where L2 is the operator for square of angular momentum and I the moment of inertia. The eigenvalues and eigenfunctions of L2 are known: Lylnu =t(1+1)ay," , where m.--1, , +1 a) Calculate the canonical partition function : of a rigid rotor. Hint: Replace summation over by integral. b) What is the probability that...
please help
4.) Calculate the rotational partition function for Hy at 1000 K, where B=60.589 cm 1
1. Calculate (a) the thermal wave-length (in pm) and (b) the translational partition function of H atom in a cubic box of side 1.0 cm at 300 K. (c) Can a hydrogern molecule be considered as a classical system (as a diatomic molecule in whiclh hydrogen atoms behave classically) at this temperature? Explain why.
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