IGNOU MCH 18 SOLVED ASSIGNMENT

Ques 1.

 State Heisenberg's Uncertainty Principle and write its mathematical expression.

Ques 2.

What is meant by an orthonormal set of wavefunctions.

Ques 3.

The ground state energy of a particle in a 1-D box cannot be zero? Comment.

Ques 4.

Give the boundary conditions where the wavefunction for a particle confined to move in a three-dimensional box must be zero.

Ques 5.

Calculate the number of radial nodes for a 3d orbital.

Ques 6.

Sketch the wavefunction for the first excited state of a quantum harmonic oscillator.

Ques 7.

Give the energy expression for a rigid rotor in three dimensions. What is the significance of J = 0?

Ques 8.

What is the difference between probability density and probability. 

Ques 9.

What is the difference between probability density and probability. 

Ques 10.

Outline the important experimental observations on photoelectric effect. How did Einstein's explain the experimental observation of threshold frequency in the context of photoelectric effect? 

Ques 11.

 Show that the (3, 3, 3) and (5, 1, 1) energy states for a particle in three-dimensional box are degenerate. 

Ques 12.

A particle confined to move in a one-dimensional box of length L, is in its ground state. Calculate the probability, p, for finding the particle between x=0.25L and x = 0.75L. 

Ques 13.

Calculate the expectation (average) value of the energy of a particle of mass m confined to move in a one-dimensional box of width a and infinite height with potential energy zero inside the box. The normalized wave function of the particle is

ψₙ(x) = (2/a)¹/² sin(nπx/a)

Where, n = 1, 2, 3...

Ques 14.

 How many quantum numbers emerge as a consequence of solving the Schrodinger's wave equation for hydrogen like ions? 

Ques 15.

Calculate the most probable distance, rₘₚ, of the electron from the nucleus in the ground state of hydrogen atom, given that the normalized ground state wave function is

Ques 16.

Calculate H₀(ξ), H₁(ξ), H₂(ξ) by using following Rodrigue formula. 

Hₙ(ξ) = (-1)ⁿe^(ξ²) (dⁿ/dξⁿ)(e⁻^(ξ²))

Ques 17.

 Which state of the triply ionized beryllium (Be³⁺) has the same orbital radius as that of the ground state of hydrogen atom. 

Ques 18.

Calculate the probability for the electron to be found in the region r = a₀ to r = ∞ for 1s orbital of H atom. For 1s orbital the normalised wavefunction is defined as

ψ₁ₛ = (2/a₀³/²) exp(-r/a₀) (4)

(b) Show that [L̂², L̂ₓ] = [L̂², L̂y] = [L̂², L̂z] = 0 

Ques 19.

Find the energy of n = 2 level of helium ion, He⁺ in eV. Assume that its reduced mass is same as that for hydrogen atom.

Ques 20.

 What are the main differences between the spin and orbital angular momentum?

Ques 21.

The expectation energy as determined by the variation method cannot be less than the true ground state energy of the system. Comment.

Ques 22.

 What are Slater type functions for multielectron atoms? What is their importance?

Ques 23.

Which of the perturbation methods used gives a better estimate of the ground state energy of helium atom?

Ques 24.

Give the difference between symmetry element and symmetry operation.

Ques 25.

Give the difference between symmetry element and symmetry operation.

Ques 26.

What are the factors that determine the energy of molecular orbitals?

Ques 27.

What are the factors that determine the energy of molecular orbitals?

Ques 28.

What is Hückel's assumption for an exchange integral?

Ques 29.

Write the Slater determinant for the ground state for lithium atom. 

Ques 30.

Why the approximation methods are necessary in quantum chemistry? Give the difference between variation method and the Perturbation theory. 

Ques 31.

Consider the following trial wavefunction for a particle of mass m confined to move in a one-dimensional box of length, L.

ψ = ax(L – x)²
Determine the corresponding energy by using variation theorem. 

Ques 32.

Formulate the matrix representation for reflection of a vector through xy plane. 

Ques 33.

Deduce the point group of all the isomers of difluoroethane. 

Ques 34.

Deduce the point group of all the isomers of difluoroethane. 

Ques 35.

Define mathematical groups and outline their characteristics. 

Ques 36.

Write the complete Hamiltonian for the Hydrogen Molecule and specify different terms involved. 

Ques 37.

Draw a schematic diagram of the variation of E⁺ and E⁻ for hydrogen molecule as a function of internuclear distance. 

Ques 38.

Formulate the spatial wavefunction for hydrogen molecule using the ground state wavefunction of hydrogen molecule ion. 

Ques 39.

Write down the molecular orbital configuration of B₂⁺ ion. 

Ques 40.

Write down the wave function for the nonbonding molecular orbital for a heteronuclear diatomic molecule AB assuming that the electron on an average spend 90% of its time on nucleus A and 10% of its time on nucleus B. 

Ques 41.

One of the three HMO molecular orbitals (MOs) for allyl radical is given below:

ψ = ½ χ₁ – (1/√2) χ₂ + ½ χ₃

Find out all three MOs of allyl radical and arrange them in order of increasing energy. Justify your answer. 

Ques 42.

One of the three HMO molecular orbitals (MOs) for allyl radical is given below:

ψ = ½ χ₁ – (1/√2) χ₂ + ½ χ₃

Find out all three MOs of allyl radical and arrange them in order of increasing energy. Justify your answer. 

Ques 43.

 State Heisenberg's Uncertainty Principle and write its mathematical expression.

Ques 44.

What is meant by an orthonormal set of wavefunctions.

Ques 45.

The ground state energy of a particle in a 1-D box cannot be zero? Comment.

Ques 46.

Give the boundary conditions where the wavefunction for a particle confined to move in a three-dimensional box must be zero.

Ques 47.

Calculate the number of radial nodes for a 3d orbital.

Ques 48.

Sketch the wavefunction for the first excited state of a quantum harmonic oscillator.

Ques 49.

Give the energy expression for a rigid rotor in three dimensions. What is the significance of J = 0?

Ques 50.

What is the difference between probability density and probability. 

Ques 51.

What is the difference between probability density and probability. 

Ques 52.

Outline the important experimental observations on photoelectric effect. How did Einstein's explain the experimental observation of threshold frequency in the context of photoelectric effect? 

Ques 53.

 Show that the (3, 3, 3) and (5, 1, 1) energy states for a particle in three-dimensional box are degenerate. 

Ques 54.

A particle confined to move in a one-dimensional box of length L, is in its ground state. Calculate the probability, p, for finding the particle between x=0.25L and x = 0.75L. 

Ques 55.

Calculate the expectation (average) value of the energy of a particle of mass m confined to move in a one-dimensional box of width a and infinite height with potential energy zero inside the box. The normalized wave function of the particle is

ψₙ(x) = (2/a)¹/² sin(nπx/a)

Where, n = 1, 2, 3...

Ques 56.

 How many quantum numbers emerge as a consequence of solving the Schrodinger's wave equation for hydrogen like ions? 

Ques 57.

Calculate the most probable distance, rₘₚ, of the electron from the nucleus in the ground state of hydrogen atom, given that the normalized ground state wave function is

Ques 58.

Calculate H₀(ξ), H₁(ξ), H₂(ξ) by using following Rodrigue formula. 

Hₙ(ξ) = (-1)ⁿe^(ξ²) (dⁿ/dξⁿ)(e⁻^(ξ²))

Ques 59.

 Which state of the triply ionized beryllium (Be³⁺) has the same orbital radius as that of the ground state of hydrogen atom. 

Ques 60.

Calculate the probability for the electron to be found in the region r = a₀ to r = ∞ for 1s orbital of H atom. For 1s orbital the normalised wavefunction is defined as

ψ₁ₛ = (2/a₀³/²) exp(-r/a₀) (4)

(b) Show that [L̂², L̂ₓ] = [L̂², L̂y] = [L̂², L̂z] = 0 

Ques 61.

Find the energy of n = 2 level of helium ion, He⁺ in eV. Assume that its reduced mass is same as that for hydrogen atom.

Ques 62.

 What are the main differences between the spin and orbital angular momentum?

Ques 63.

The expectation energy as determined by the variation method cannot be less than the true ground state energy of the system. Comment.

Ques 64.

 What are Slater type functions for multielectron atoms? What is their importance?

Ques 65.

Which of the perturbation methods used gives a better estimate of the ground state energy of helium atom?

Ques 66.

Give the difference between symmetry element and symmetry operation.

Ques 67.

Give the difference between symmetry element and symmetry operation.

Ques 68.

What are the factors that determine the energy of molecular orbitals?

Ques 69.

What are the factors that determine the energy of molecular orbitals?

Ques 70.

What is Hückel's assumption for an exchange integral?

Ques 71.

Write the Slater determinant for the ground state for lithium atom. 

Ques 72.

Why the approximation methods are necessary in quantum chemistry? Give the difference between variation method and the Perturbation theory. 

Ques 73.

Consider the following trial wavefunction for a particle of mass m confined to move in a one-dimensional box of length, L.

ψ = ax(L – x)²
Determine the corresponding energy by using variation theorem. 

Ques 74.

Formulate the matrix representation for reflection of a vector through xy plane. 

Ques 75.

Deduce the point group of all the isomers of difluoroethane. 

Ques 76.

Deduce the point group of all the isomers of difluoroethane. 

Ques 77.

Define mathematical groups and outline their characteristics. 

Ques 78.

Write the complete Hamiltonian for the Hydrogen Molecule and specify different terms involved. 

Ques 79.

Draw a schematic diagram of the variation of E⁺ and E⁻ for hydrogen molecule as a function of internuclear distance. 

Ques 80.

Formulate the spatial wavefunction for hydrogen molecule using the ground state wavefunction of hydrogen molecule ion. 

Ques 81.

Write down the molecular orbital configuration of B₂⁺ ion. 

Ques 82.

Write down the wave function for the nonbonding molecular orbital for a heteronuclear diatomic molecule AB assuming that the electron on an average spend 90% of its time on nucleus A and 10% of its time on nucleus B. 

Ques 83.

One of the three HMO molecular orbitals (MOs) for allyl radical is given below:

ψ = ½ χ₁ – (1/√2) χ₂ + ½ χ₃

Find out all three MOs of allyl radical and arrange them in order of increasing energy. Justify your answer. 

Ques 84.

One of the three HMO molecular orbitals (MOs) for allyl radical is given below:

ψ = ½ χ₁ – (1/√2) χ₂ + ½ χ₃

Find out all three MOs of allyl radical and arrange them in order of increasing energy. Justify your answer. 

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