Virtual Labs

1. What does the solution to the time-independent Schrödinger’s Wave Equation represent?

a: The exact location of the electron Explanation

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b: The probability of locating the electron in space Explanation

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c: The velocity of the electron Explanation

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d: The total charge of the electron Explanation

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2. Which of the following best describes a finite potential well?

a: A system where the particle is completely free Explanation

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b: A region where the potential energy is zero everywhere Explanation

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c: A confined region with finite potential barriers on either side Explanation

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d: A region with infinite walls on both sides Explanation

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3. In the infinite potential well problem, where is the probability of finding the particle zero?

a: At the center of the well Explanation

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b: Outside the well Explanation

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c: Everywhere inside the well Explanation

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d: There is no zero probability point Explanation

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4. What condition leads to discrete energy levels in a quantum well?

a: Uniform electric field Explanation

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b: Boundary conditions on the wavefunction Explanation

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c: Thermal vibrations of the lattice Explanation

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d: Presence of photons Explanation

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5. In quantum mechanics, which of the following is always true about a bound particle’s wavefunction?

a: It is infinite everywhere Explanation

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b: It is discontinuous at the boundaries Explanation

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c: It is always real Explanation

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d: It is continuous and normalizable Explanation

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6. Which mathematical operation in the SWE leads to energy quantization?

a: Squaring the wavefunction Explanation

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b: Differentiating the potential Explanation

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c: Applying boundary conditions Explanation

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d: Adding the kinetic and potential energy terms Explanation

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7. If a particle is in the second energy level (n=2) of an infinite potential well of width L, its energy is:

a: Twice that of n=1 Explanation

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b: Four times that of n=1 Explanation

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c: Same as n=1 Explanation

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d: Not quantized Explanation

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8. What physical phenomenon allows a particle to be found outside a finite potential well?

a: Superposition Explanation

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b: Decoherence Explanation

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c: Quantum tunneling Explanation

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d: Coulomb repulsion Explanation

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9. What happens to the allowed energy levels in an infinite potential well as the width of the well increases?

a: They increase Explanation

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b: They decrease Explanation

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c: They stay the same Explanation

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d: They become continuous Explanation

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Schrodinger Wave Equation and Solution