Solved Schr_dinger Wave Equation (Quantum Chemistry)

Schr_dinger Wave Equation MCQs for Competitive Exams

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Topic Notes: Schr_dinger Wave Equation

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For a particle of mass m in a one-dimensional box of length l, what is the energy difference between the levels corresponding to the 3-node and 2-node eigenfunctions, expressed in units of h^2/(8ml^2)?

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The wave function for a quantum mechanical particle in a one-dimensional box of length a is given by $$\psi = A\sin \frac{{\pi x}}{a}.$$ The value of A for a box of length 200 nm is

4 × 104(nm)2

0.1 (nm)-1/2

10$$\sqrt 2 $$ (nm)1/2

$$\sqrt 2 $$ /10 (nm)-1/2

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Are the eigenfunctions defined by ψn(x) = sqrt(2/a) * sin(nπx/a) for a particle in a 1D box (0 ≤ x ≤ a) orthogonal and normalized?

both orthogonal and normalized

normalized

orthogonal

unnormalized

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Why is the function ψ(x) = exp(ax^2) (where a > 0) considered an unacceptable wavefunction for a bound physical system?

it is not normalizable

it is multi-valued

it is not continuous

All of these

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The vibrational partition function for a molecule which can be described as a simple harmonic oscillator with fundamental frequency $$\nu $$ is given by

$${\left[ {1 - \exp \left( { - \frac{{h\nu }}{{{K_B}T}}} \right)} \right]^{ - 1}}$$

$$\exp \left( { - \frac{{h\nu }}{{{K_B}T}}} \right)$$

$$\exp \left( { - \frac{{h\nu }}{{2{K_B}T}}} \right){\left[ {1 - \exp \left( { - \frac{{h\nu }}{{{K_B}T}}} \right)} \right]^{ - 1}}$$

$$\exp \left( { - \frac{{h\nu }}{{{K_B}T}}} \right){\left[ {1 - \exp \left( { - \frac{{h\nu }}{{{K_B}T}}} \right)} \right]^{ - 1}}$$

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A particle is confined to a 1D box of length L = 1 mm. If the length increases by ΔL = 10^-9 m, what is the percentage change in the ground state energy?

2 × 10-2

2 × 10-7

2 × 10-4

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For which quantum mechanical system does the energy (E) increase quadratically with the quantum number (n)?

one-dimensional harmonic oscillator

particle in a one-dimensional box

hydrogen atom

rigid rotor

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Consider a particle of mass m moving in a one-dimensional box under the potential V = 0 for 0 ≤ x ≤ a and V = $$\infty $$ outside the box. When the particle is in its lowest energy state, the average momentum (< px>) of the particle is

$$ < {p_x} > = \frac{h}{{2a}}$$

$$ < {p_x} > = \frac{h}{a}$$

$$ < {p_x} > = 0$$

$$ < {p_x} > = \frac{h}{{2\pi a}}$$

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How many extrema (maxima and minima) does the harmonic oscillator wavefunction ψ(x) = Nx * exp(-ax^2/2) possess?

two maxima, one minimum only

one maximum only

two maxima, two minima only

one maximum, one minimum only

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An electron of mass m is confined to a one-dimensional box of length b. If it makes a radiative transition from second excited state to the ground state/the frequency of the photon emitted is

$$\frac{h}{{m{b^2}}}$$

$$\frac{{3h}}{{8m{b^2}}}$$

$$\frac{{2h}}{{8m{b^2}}}$$

$$\frac{{9h}}{{8m{b^2}}}$$

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Schr_dinger Wave Equation MCQs for Competitive Exams

Schr_dinger Wave Equation MCQs for Competitive Exams

Topic Notes: Schr_dinger Wave Equation

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