Quantum Chemistry Question with detailed solution pdf link| Hydrogen Atom, Box problem

Q and A in topic Huckel approximation: π- electron systems, Particle inbox, Simple Harmonic oscillator (SHO), Rigid rotor, Hydrogen atom, etc.

Quantum Chemistry-1 Q&A for CSIR NET, GATE, IIT JAM

Hello everyone today we will discuss Quantum chemistry questions and answer series -1 with detailed solutions for CSIR NET, GATE, IIT JAM, and other entrance exam aspirants. A chemistry student must read quantum mechanics chapters. For atomic real structure and function, determination requires a good knowledge of Quantum chemistry. In this article below our team provides questions with detailed solutions free download pdf file go through and download.

Quantum Chemistry Basic Topics

In quantum chemistry, the most common topics are Plank Blackbody Radiation law, de Broglie wave function, Postulates of quantum mechanics, time-dependent and time-independent Schrödinger equation, Interpretation of Bohr’s First Postulate, Particle inbox: 1D, 2D, 3D box, Simple Harmonic oscillator (SHO), Rigid rotor, Hydrogen atom, etc.

And other topics in quantum mechanics are the Approximation method: The variational method, first order, and second-order Perturbation theory, Huckel approximation: π- electron systems, etc.

Related: Physical Chemistry Questions with Solution -Quantum Chemistry, Thermodynamics, and Chemical Kinetics -Mixup.

Which books are best for Quantum chemistry?

We have to recommend a textbook for quantum mechanics: Quantum Chemistry Donald A McQuarrie. And another popular physical chemistry book is Physical Chemistry Atkins - here quantum mechanics chapters are an easy-to-discuss and question-solving approach.

Quantum chemistry Problems with detailed solutions

Including all Quantum chemistry questions are maybe previous year Questions on GATE, CSIR NET, and other entrance examinations. A chemistry student or an entrance examination aspirant must practice these types of questions.

Q.1. The highest energy π – molecular orbital for the allyl system is

1) 1/√2 χ_1+1/2 χ_2+1/√2 χ_3                             2)  1/√2 χ_1-1/√2 χ_3

3)  1/2 χ_1-1/√2 χ_2+1/2 χ_3                               4)1/√2 χ_1-1/2 χ_2-1/√2 χ_3

This is the Quantum Chemistry Q.1.
Quantum Chemistry Q.1.

Answer:  3)  1/2 χ_1-1/√2 χ_2+1/2 χ_3

Hints:   Highest energy π- molecular orbital corresponds to a higher number of nodes. Therefore, the molecular orbital energy is directly proportional to the number of molecular nodes.

Highest energy π- molecular orbital is correspond to a higher number of nodes. π – molecular orbital for the allyl system.
Allyl system MO energy.

We see in option (3) that the numbers of nodes are higher than other orbitals. According to the higher number of nodes, this molecular orbital exists in higher energy.   

Q.2. The energy functional from a trial wave function is E(α)= 〖(α〗^2-3α)/6

The variationally optimized energy is

1)  -1/2            2)  -3/8

3)   3/2                4)   3/8

this is the Quantum chemistry Q.2
Quantum chemistry Q.2

Answer:   2)  -3/8

Hints:   For variationally optimized energy: we follow three steps 


Differentiate equation E(α)= 〖(α〗^2-3α)/6 concerning α we get,







Put the value of α in the energy equation.


=[9/4-9/2]/6= -3/8

This is the variationally optimized energy of the given equation.

Q.3. An unnormalized wave function of the hydrogen atom is given by r^2 e^(-r/3) (3〖cos〗^2 θ-1).  The three quantum numbers, n, l, and m, associated with this orbital are, respectively.

1) 2, 2, 0

2) 2, 1, 1

3) 3, 2, 0

4) 3, 1, 1

This is the Quantum chemistry Q.3
Quantum chemistry Q.3

Answer:   3) 3, 2, 0

Hints:   Unnormalized Wave function of the hydrogen atom

〖Ψ=r〗^2 e^(-r/3) (3〖cos〗^2 θ-1)

The Radial part of this equation is 〖R(r)=r〗^2 e^(-r/3)  we get the value of n and l. 

We know that R(r)=e^(-zr/na)  where z =1, and a =1. We get n =3. In the 〖R(r)=r〗^2 part we get l =2 (the minimum power of r is equal to l).

At this hole equation looks like this 

Ψ=r〗^2 e^(-r/3) (3〖cos〗^2 θ-1) e^(-imφ)

Now we follow through the above equation compared to the given wave function. At the m = 0, then the exponential hole factor becomes 1.

Hence, the three quantum numbers, n, l, and m, associated with this orbital are, respectively 3, 2, and 0.

Q.4. A satisfactory spin wave function for an excited helium atom is

1) 1/√2 [α(1)β(2)]+[α(2)β(1)]

2) [α(1)β(2)]

3) 1/√2 [α(1)α(2)]+[β(1)β(2)]

4) [α(2)β(1)]

Quantum chemistry Q.4
Quantum chemistry Q.4

Answer:   1) 1/√2 [α(1)β(2)]+[α(2)β(1)]

Hints:   in considering α is 

Q.5. For a particle of mass m in a one-dimensional box of length 2L, the energy of the level corresponding to n = 8 is

1)  h^2/(8mL^2 )

2)  h^2/(32mL^2 )

3)  h^2/(mL^2 )

4) 〖2h〗^2/(mL^2 )

This is the Quantum chemistry Q.5
Quantum chemistry Q.5

Answer:     4)〖2h〗^2/(mL^2 )

Hints:   A particle of mass m in a one-dimensional box of length L, the energy equation is

E=(n^2 h^2)/(8mL^2 )

When n =8 and box length L = 2L.

E=(8^2 h^2)/(8m〖(2L)〗^2 )=(8h^2)/(m4L^2 )=〖2h〗^2/(mL^2 )

This is the energy of a one-dimensional box.

Solve Related Questions Paper: Quantum Chemistry Questions with solutions -Physical Chemistry Mixup Questions-Thermodynamics, Chemical Kinetics.

PDF Link for Quantum Chemistry Questions series

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