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Chapter 39: Q4P (page 1215)
An electron, trapped in a one-dimensional infinite potential well 250 pm wide, is in its ground state. How much energy must it absorb if it is to jump up to the state with ?
90.3 eV
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A proton and an electron are trapped in identical one-dimensional infinite potential wells; each particle is in its ground state. At the center of the wells, is the probability density for the proton greater than, less than, or equal to that of the electron?
figure 39-28 shows the energy-level diagram for a finite, one-dimensional energy well that contains an electron. The nonquantized region begins at . Figure 39-28b gives the absorption spectrum of the electron when it is in the ground state鈥攊t can absorb at the indicated wavelengths: and for any wavelength less than . What is the energy of the first excited state?
The wave functions for the three states with the dot plots shown in Fig. 39-23, which have n = 2 , l = 1 , and 0, and , are
in which the subscripts on give the values of the quantum numbers n , l , and the angles and are defined in Fig. 39-22. Note that the first wave function is real but the others, which involve the imaginary number i, are complex. Find the radial probability density P(r) for (a) and (b) (same as for ). (c) Show that each P(r) is consistent with the corresponding dot plot in Fig. 39-23. (d) Add the radial probability densities for , , and and then show that the sum is spherically symmetric, depending only on r.
A hydrogen atom in a state having a binding energy (the energy required to remove an electron) of 0.85 eV makes a transition to a state with an excitation energy (the difference between the energy of the state and that of the ground state) of . (a) What is the energy of the photon emitted as a result of the transition? What are the (b) higher quantum number and (c) lower quantum number of the transition producing this emission?
An electron in the n = 2 state in the finite potential well of Fig. 39-7 absorbs 400 eV of energy from an external source. Using the energy-level diagram of Fig. 39-9, determine the electron鈥檚 kinetic energy after this absorption, assuming that the electron moves to a position for which x > L.
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