1. For a particle in a box problem, the probability of finding the particle outside the box is (a) Not defined (b) Zero (c) One (d) Infinity (e) None of the above 2. The energy levels of a particle in a box problem are: (a) Dependent on time (b) All the same (c) Normalized (d) Quantized (e) None of the above 3. An electron confined to an infinite square well potential of length 0.4 nm is in its second excited state. (a) What is the wavelength of the electron in the third excited state? (b) What is the wavelength of the emitted photon when the electron is de-excited to the ground state? (c) Draw a sketch of the electron's wavefunction in third excited state.
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For a particle in a box problem, the probability of finding the particle outside the box is b) Zero. This is because the particle is confined within the boundaries of the box and cannot exist outside of it. Show moreā¦
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An electron is confined to a one-dimensional box of length $L$. When the electron makes a transition from its first excited state to the ground state, it emits a photon of energy 0.20 eV. (a) What is the ground-state energy (in electron-volts) of the electron in this box? (b) What are the energies (in electron-volts) of the photons that can be emitted when the electron starts in its third excited state and makes transitions downwards to the ground state (either directly or through intervening states)? (c) Sketch the wave function of the electron in the third excited state. (d) If the box were somehow made longer, how would the electron's new energy level spacings compare with its old ones? (Would they be greater, smaller, or the same? Or is more information needed to answer this question? Explain.)
An electron is confined to a one-dimensional box of length $L$. When the electron makes a transition from its first excited state to the ground state, it emits a photon of energy $0.20 \mathrm{eV}$. (a) What is the ground-state energy (in $\mathrm{eV}$ ) of the electron in this box? (b) What are the energies (in eV) of the photons that can be emitted when the electron starts in its third excited state and makes transitions downwards to the ground state (either directly or through intervening states)? (c) Sketch the wave function of the electron in the third excited state. (d) If the box were somehow made longer, how would the electron's new energy level spacings compare with its old ones? (Would they be greater, smaller, or the same? Or is more information needed to answer this question? Explain.)
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