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. 

Ques 85.

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

Ques 86.

What is meant by an orthonormal set of wavefunctions.

Ques 87.

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

Ques 88.

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

Ques 89.

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

Ques 90.

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

Ques 91.

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

Ques 92.

What is the difference between probability density and probability. 

Ques 93.

What is the difference between probability density and probability. 

Ques 94.

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 95.

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

Ques 96.

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 97.

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 98.

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

Ques 99.

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 100.

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

Hₙ(ξ) = (-1)ⁿe^(ξ²) (dⁿ/dξⁿ)(e⁻^(ξ²))

Ques 101.

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

Ques 102.

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 103.

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 104.

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

Ques 105.

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

Ques 106.

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

Ques 107.

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

Ques 108.

Give the difference between symmetry element and symmetry operation.

Ques 109.

Give the difference between symmetry element and symmetry operation.

Ques 110.

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

Ques 111.

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

Ques 112.

What is Hückel's assumption for an exchange integral?

Ques 113.

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

Ques 114.

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

Ques 115.

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 116.

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

Ques 117.

Deduce the point group of all the isomers of difluoroethane. 

Ques 118.

Deduce the point group of all the isomers of difluoroethane. 

Ques 119.

Define mathematical groups and outline their characteristics. 

Ques 120.

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

Ques 121.

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

Ques 122.

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

Ques 123.

Write down the molecular orbital configuration of B₂⁺ ion. 

Ques 124.

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 125.

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 126.

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 127.

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

Ques 128.

What is meant by an orthonormal set of wavefunctions.

Ques 129.

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

Ques 130.

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

Ques 131.

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

Ques 132.

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

Ques 133.

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

Ques 134.

What is the difference between probability density and probability. 

Ques 135.

What is the difference between probability density and probability. 

Ques 136.

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 137.

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

Ques 138.

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 139.

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 140.

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

Ques 141.

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 142.

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

Hₙ(ξ) = (-1)ⁿe^(ξ²) (dⁿ/dξⁿ)(e⁻^(ξ²))

Ques 143.

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

Ques 144.

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 145.

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 146.

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

Ques 147.

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

Ques 148.

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

Ques 149.

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

Ques 150.

Give the difference between symmetry element and symmetry operation.

Ques 151.

Give the difference between symmetry element and symmetry operation.

Ques 152.

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

Ques 153.

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

Ques 154.

What is Hückel's assumption for an exchange integral?

Ques 155.

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

Ques 156.

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

Ques 157.

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 158.

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

Ques 159.

Deduce the point group of all the isomers of difluoroethane. 

Ques 160.

Deduce the point group of all the isomers of difluoroethane. 

Ques 161.

Define mathematical groups and outline their characteristics. 

Ques 162.

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

Ques 163.

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

Ques 164.

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

Ques 165.

Write down the molecular orbital configuration of B₂⁺ ion. 

Ques 166.

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 167.

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 168.

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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