Q1 · 2020 · 2 marks
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Answer: (a)
CSIR NET Chemical Science — Quantum Chemistry previous year questions
22 questions · 2011–2020 · all with verified answer · last checked 2026-11-06
Q2 · 2018 · 2 marks
A particle is in a state \phi = \psi_1 + 3\psi_2 where \psi_1 and \psi_2 are eigenfunctions of the Hamiltonian of the particle with eigenvalues E_1 and E_2, respectively. The average energy of the particle in the state \phi is
- (a) (E_1 + 9E_2)/10
- (b) (E_1 + 3E_2)
- (c) (E_1 + 9E_2)/14
- (d) (E_1 + 3E_2)/10
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Answer: (a)
Q3 · 2018 · 2 marks
Which of these is not a suitable unnormalized wave function for the excited 1s 2s electron configuration of the helium atom ?
- (a) [1s(1)2s(2) - 2s(1)1s(2)][\beta(1)\beta(2)]
- (b) [1s(1)2s(2) + 2s(1)1s(2)][\alpha(1)\beta(2) - \beta(1)\alpha(2)]
- (c) [1s(1)2s(2) - 2s(1)1s(2)][\alpha(1)\beta(2) + \beta(1)\alpha(2)]
- (d) [1s(1)2s(2) + 2s(1)1s(2)][\alpha(1)\beta(2)]
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Answer: (d)
Q4 · 2017 · 2 marks
The correct statement about the difference of second and first excited state energies (\Delta E) of a particle in 1-D, 2-D square and 3-D cubic boxes with same length for each, is
- (a) \Delta E (1-D box) = \Delta E (2-D box) = \Delta E (3-D box)
- (b) \Delta E (1-D box) > \Delta E (2-D box) > \Delta E (3-D box)
- (c) \Delta E (1-D box) > \Delta E (2-D box) = \Delta E (3-D box)
- (d) \Delta E (1-D box) < \Delta E (2-D box) < \Delta E (3-D box)
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Answer: (c)
Q5 · 2016 · 2 marks
Average value of momentum for the ground state of a particle in a 1-d box is zero because
- (a) [p, H] = 0
- (b) V (potential) = 0
- (c) H is hermitian
- (d) the state is bound and stationary
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Answer: (d)
Q6 · 2016 · 2 marks
For a hermitian operator A, which does NOT commute with the Hamiltonian H, let \psi_1 be an eigenfunction of A and \psi_2 be an eigenfunction of H. The correct statement regarding the average value of the commutator of A with H ([A,H]) is
- (a) both \langle\psi_1|[A,H]|\psi_1\rangle and \langle\psi_2|[A,H]|\psi_2\rangle are non-zero
- (b) only \langle\psi_1|[A,H]|\psi_1\rangle is zero, but \langle\psi_2|[A,H]|\psi_2\rangle is non-zero
- (c) only \langle\psi_2|[A,H]|\psi_2\rangle is zero, but \langle\psi_1|[A,H]|\psi_1\rangle is non-zero
- (d) both \langle\psi_1|[A,H]|\psi_1\rangle and \langle\psi_2|[A,H]|\psi_2\rangle are zero
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Answer: (d)
Q7 · 2016 · 2 marks
The correct normalized wave function for one of the sp^2 hybrid orbitals is
- (a) \frac{1}{3}\psi_{2s} - \frac{1}{3}\psi_{2px} + \frac{1}{3}\psi_{2py}
- (b) \frac{1}{\sqrt{3}}\psi_{2s} - \frac{2}{\sqrt{3}}\psi_{2px} + \frac{1}{\sqrt{6}}\psi_{2py}
- (c) \frac{1}{\sqrt{3}}\psi_{2s} - \frac{1}{\sqrt{2}}\psi_{2px} + \frac{1}{\sqrt{6}}\psi_{2py}
- (d) \frac{1}{\sqrt{3}}\psi_{2s} - \frac{1}{2\sqrt{3}}\psi_{2px} + \frac{1}{\sqrt{6}}\psi_{2py}
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Answer: (c)
Q8 · 2016 · 2 marks
The eigenfunctions of the Hamiltonian \mathbf{H}(\mathbf{H}=\mathbf{T}+\mathbf{V}) of a harmonic oscillator are (where \mathbf{T} and V are kinetic energy and potential energy operators, respectively)
- (a) eigenfunctions of T as well as V
- (b) eigenfunctions of T , but not of V
- (c) eigenfunctions of V, but not of T
- (d) eigenfunctions of neither T nor V
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Answer: (d)
Q9 · 2015 · 2 marks
The simplest ground-state VB wave function of a diatomic molecule like HCl is written as \psi = \psi_H(1s,1)\psi_{Cl}(3p_z,2) + B where B stands for
- (a) \psi_H(3p_z,2)\psi_{Cl}(1s,1)
- (b) \psi_H(1s,2)\psi_{Cl}(3p_z,1)
- (c) \psi_{Cl}(1s,2)\psi_{Cl}(3p_z,1)
- (d) \psi_{Cl}(1s,2)\psi_H(3p_z,1)
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Answer: (b)
Q10 · 2014 · 2 marks
If the ionization energy of H atom is x, the ionization energy of \mathrm{Li^{+2}} is
- (a) 2x
- (b) 3x
- (c) 9x
- (d) 27x
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Answer: (c)
Q11 · 2013 · 2 marks
The wave function \psi of a certain system is the linear combination
\psi = \sqrt{\frac{1}{4}}\,\psi_1 + \sqrt{\frac{3}{4}}\,\psi_2
where \psi_1 and \psi_2 are energy eigen functions with eigen values (non-degenerate) E_1 and E_2 respectively. What is the probability that the system energy will be observed to be E_1 ? - (a) \sqrt{\frac{3}{16}}
- (b) \frac{3}{4}
- (c) \frac{1}{4}
- (d) \sqrt{\frac{1}{4}}
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Answer: (c)
Q12 · 2013 · 2 marks
Identify the Huckel determinant for cyclobutadiene
- (a) \begin{vmatrix} \alpha-E & \beta & 0 & 0 \\ \beta & \alpha-E & \beta & 0 \\ 0 & \beta & \alpha-E & \beta \\ 0 & 0 & \beta & \alpha-E \end{vmatrix}
- (b) \begin{vmatrix} \alpha-E & \beta & 0 & \beta \\ \beta & \alpha-E & \beta & 0 \\ 0 & \beta & \alpha-E & \beta \\ \beta & \beta & 0 & \alpha-E \end{vmatrix}
- (c) \begin{vmatrix} \alpha-E & \beta & 0 & \beta \\ \beta & \alpha-E & \beta & 0 \\ 0 & \beta & \alpha-E & \beta \\ \beta & 0 & \beta & \alpha-E \end{vmatrix}
- (d) \begin{vmatrix} \alpha-E & \beta & 0 & \beta \\ \beta & \alpha-E & \beta & 0 \\ 0 & \beta & \alpha-E & \beta \\ 0 & 0 & \beta & \alpha-E \end{vmatrix}
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Answer: (c)
Q13 · 2013 · 2 marks
Consider a two-dimensional harmonic oscillator with potential energy
V(x, y)=\frac{1}{2} k_{x} x^{2}+\frac{1}{2} k_{y} y^{2}
If \boldsymbol{\psi}_{\mathbf{n x}}(\mathbf{x}) and \boldsymbol{\psi}_{\mathbf{n y}}(\mathbf{y}) are the eigensolutions and \mathbf{E}_{\mathbf{n x}} and \mathbf{E}_{\mathbf{n y}} are the eigenvalues of harmonic oscillator problem in x and y direction with potential \frac{1}{2} k_{x} x^{2} and \frac{1}{2} k_{y} y^{2} respectively, the wave function and eigenvalues of the above two-dimensional harmonic oscillator problem are - (a) \boldsymbol{\psi}_{\mathbf{n x}, \mathbf{n y}}=\boldsymbol{\psi}_{\mathbf{n x}}(\mathbf{x})+\boldsymbol{\psi}_{\mathbf{n y}}(\mathbf{y})
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Answer: (c)
Q14 · 2013 · 2 marks
The most probable value of 'r' for an electron in 1s orbital of hydrogen atom is
- (a) a_0/2
- (b) a_0
- (c) \sqrt{2}\,a_0
- (d) 3a_0/2
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Answer: (b)
Q15 · 2013 · 2 marks
The angular momentum operator \hat{L}_y
- (a) -\frac{\hbar}{i}\left(y\frac{\partial}{\partial z} - z\frac{\partial}{\partial y}\right)
- (b) \frac{\hbar}{i}\left(z\frac{\partial}{\partial x} - x\frac{\partial}{\partial z}\right)
- (c) \frac{-i\hbar}{2m}\frac{\partial}{\partial x}
- (d) \frac{\hbar}{i}\left(z\frac{\partial}{\partial x} - y\frac{\partial}{\partial y}\right)
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Answer: (b)
Q16 · 2013 · 2 marks
The energy for a single electron excitation in cyclopropenium cation in Hückel theory is
- (a) \beta
- (b) 2\beta
- (c) 3\beta
- (d) 4\beta
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Answer: (c)
Q17 · 2012 · 2 marks
The probability of finding the particle in a one dimensional box of length 'L' in the region between \frac{L}{4} and \frac{3L}{4} for quantum number n = 1 is:
- (a) \frac{1}{2}
- (b) \frac{1}{2} + \frac{1}{\pi}
- (c) \frac{1}{2} - \frac{1}{\pi}
- (d) \frac{2}{3}
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Answer: (b)
Q18 · 2012 · 2 marks
Using Hückel molecular orbital approximation, the two roots of secular equation of ethene are
- (a) \alpha + \sqrt{2}\beta, \alpha - \sqrt{2}\beta
- (b) \alpha + \beta, \alpha
- (c) \alpha + \beta, \alpha - \beta
- (d) \alpha + 2\beta, \alpha - 2\beta
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Answer: (c)
Q19 · 2012 · 2 marks
If A and B are non-commuting hermitian operators, all eigenvalues of the operator given by the commutator [A, B] are
- (a) complex
- (b) real
- (c) imaginary
- (d) zero
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Answer: (c)
Q20 · 2012 · 2 marks
The trial wave function of a system is expanded as \psi_t = c_1\phi_1 + c_2\phi_2. The matrix elements of the Hamiltonian are \langle\phi_1|\hat{H}|\phi_1\rangle = 0; \langle\phi_1|\hat{H}|\phi_2\rangle = 2.0 = \langle\phi_2|\hat{H}|\phi_1\rangle and \langle\phi_2|\hat{H}|\phi_2\rangle = 3.0. The approximate ground-state energy of the system from the linear variational principle is
- (a) –1.0
- (b) –2.0
- (c) +4.0
- (d) +5.0
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Answer: (a)
Q21 · June 2011 · 2 marks
For a certain particle encountering a barrier, the tunneling probability is approximately e^{-10}. If the mass is halved and width of the barrier (rectangular) doubled, approximate value of the tunneling probability will be
- (a) e^{-10/\sqrt{2}}
- (b) e^{-10\sqrt{2}}
- (c) e^{-20\sqrt{2}}
- (d) e^{-10}
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Answer: (b)
Q22 · 2011 · 2 marks
Identify which of the following operators is not hermitian?
- (a) \frac{\hbar}{i}\frac{d}{dx}
- (b) i\frac{d^2}{dx^2}
- (c) \frac{d^2}{dx^2}
- (d) x^2
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Answer: (b)
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