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IIT JAM Exam  >  IIT JAM Tests  >  Quantum Mechanics In Three Dimensions – MSQ - IIT JAM MCQ

Quantum Mechanics In Three Dimensions – MSQ - IIT JAM MCQ


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10 Questions MCQ Test - Quantum Mechanics In Three Dimensions – MSQ

Quantum Mechanics In Three Dimensions – MSQ for IIT JAM 2024 is part of IIT JAM preparation. The Quantum Mechanics In Three Dimensions – MSQ questions and answers have been prepared according to the IIT JAM exam syllabus.The Quantum Mechanics In Three Dimensions – MSQ MCQs are made for IIT JAM 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Quantum Mechanics In Three Dimensions – MSQ below.
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Quantum Mechanics In Three Dimensions – MSQ - Question 1
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Which of the following correspond to the possible states of a hydrogen atom with n = 2. (States are designated as ψnlm.)

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The correct answers are:  

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Quantum Mechanics In Three Dimensions – MSQ - Question 2
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For particle in a 3d  box of length a. The state with energy  has :

Detailed Solution for Quantum Mechanics In Three Dimensions – MSQ - Question 2

The correct answers are: (nx, ny, nz) taking values 1, 1, 5, (nx, ny, nz) taking values 3, 3, 3, is 4 fold degenerate

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Quantum Mechanics In Three Dimensions – MSQ - Question 3
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For a particle in a 3 dimensional box

Detailed Solution for Quantum Mechanics In Three Dimensions – MSQ - Question 3

Second excited state


 

3 fold degenerate!

The correct answers are: Ground state energy is non zero, The second excited state is 3 fold degenerate

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Quantum Mechanics In Three Dimensions – MSQ - Question 4
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Consider an atomic electron in the l = 3 state. If L is the magnitude of the angular momentum, Lz is its z component, θ is the angle  makes with the z axis then :
Detailed Solution for Quantum Mechanics In Three Dimensions – MSQ - Question 4

l = 3

The correct answer is:  

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Quantum Mechanics In Three Dimensions – MSQ - Question 5
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For a quantum harmonic oscillator in 3 dimensions
Detailed Solution for Quantum Mechanics In Three Dimensions – MSQ - Question 5


 

(0, 0, 3)  →   3 state
(1, 1, 1)  →   1 state
(0, 1, 2)  →   6 state

∴   3 + 1 + 6 = 10 fold degenerate.

The correct answers are: The ground state is non degenerate, The third excited state is 10 fold degenerate

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Quantum Mechanics In Three Dimensions – MSQ - Question 6
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Consider the case of a 3 dimensional harmonic oscillator. Choose the correct statement.
Detailed Solution for Quantum Mechanics In Three Dimensions – MSQ - Question 6


can be degenerate

No symmetry in potential. Energy levels cannot be degenerate. Both have zero point energy.

The correct answers are: In case of an isotropic harmonic oscillator, the energy levels can be degenerate, In case of an anisotropic oscillator, there is no degeneracy since the potential is not symmetric, Both isotropic and anisotropic oscillators have zero point energy

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Quantum Mechanics In Three Dimensions – MSQ - Question 7
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Select the correct statement(s).
Detailed Solution for Quantum Mechanics In Three Dimensions – MSQ - Question 7

Quantum numbers l and m determine the value of angular wave function.
For a e−, as velocity is proportional to z/n, so the product of velocity and the principal quantum number will be independent of principal quantum number.
In 1925 Pauli stated that no two electrons in an atom can have same values of all four quantum numbers.
Heisenberg uncertainty principle : Δp.Δx>h/4π

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Quantum Mechanics In Three Dimensions – MSQ - Question 8
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Consider the case of particle in a 3d box and a 3d harmonic oscillator.
Detailed Solution for Quantum Mechanics In Three Dimensions – MSQ - Question 8

  (For Harmonic Oscillator)

The correct answers are: The ground state energy of 3d  simple harmonic oscillator is non zero, The ground state energy of a particle in a 3d  box is non zero.

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Quantum Mechanics In Three Dimensions – MSQ - Question 9
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For a particle in 3 dimensional box
Detailed Solution for Quantum Mechanics In Three Dimensions – MSQ - Question 9

The correct answers are: The number of quantum numbers is equal to dimensions of potential distribution, The symmetry of box leads to degeneracy, The spin quantum number does not arise from Schrodinger wave equations. Spherical polar coordinates are used in the solution of the hydrogen atom Schrodinger equation because: The Schrodinger equation is then separable into 3 ordinary differential equations. If we consider spin also for fermions then the degeneracy of energy levels become twice. 

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Quantum Mechanics In Three Dimensions – MSQ - Question 10
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For a rectangular 3 dimensional box
Detailed Solution for Quantum Mechanics In Three Dimensions – MSQ - Question 10

For a 3d  box with different edge length (ax, ay, az)

ψ will be different even if different combination   gives the same value of En. But the parity is the same

The correct answers are: Degenerate energy levels have different wave functions, Degenerate energy levels have same parity

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