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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’s kinetic energy after this absorption, assuming that the electron moves to a position for which x > L.

Short Answer

Expert verified

The electron kinetic energy after this absorption assuming that the electron moves to a position for which is x> L 56eV .

Step by step solution

01

Related concept

In the figure 39-9 the initial energy of electron is 106 eV. It absorbs addition 400eV of energy from an external source. Total energy is the sum of these two energies.

Etotal=Kj+E'

Here, Etotalis the total energy of the electron after absorbing energy from the external

is the initial energy possessed electron, and E' is the external absorbed by the electron.

Substitute 106eV for Kifor and 400 eV to find Etotal

Etotal=106eV+400eV=506eV

Thus, the total energy of the electron after absorbing energy from the external source

02

Electron’s Kinetic Energy

The total energy possessed by the electron exceeds the finite potential energy of the well thus, the electron moves to the regions x > L

the kinetic energy of the electron in the regions and is the external absorbed by x > L is,

K=Etotal-Uwell

Here, k is the kinetic energy of the electron in the region x > L

And Uwell is he potential energy of the well.

Substitute 506eV for Etotaland 450eV for Uwell to find k.

K = 506 eV - 450 eV

=56eV

Thus, the electron kinetic energy after this absorption assuming that the electron moves to a position for which x > L is 56 eV

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Most popular questions from this chapter

Figure 39-26 indicates the lowest energy levels (in electronvolts) for five situations in which an electron is trapped in a one-dimensional infinite potential well. In wells B, C, D, and E, the electron is in the ground state. We shall excite the electron in well A to the fourth excited state (at 25 eV). The electron can then de-excite to the ground state by emitting one or more photons, corresponding to one long jump or several short jumps. Which photon emission energies of this de-excitation match a photon absorption energy (from the ground state) of the other four electrons? Give then values.

The wave function for the hydrogen-atom quantum state represented by the dot plot shown in Fig. 39-21, which has n = 2 and l=ml=0, is

Ψ200(r)=142πa-3/2(2-ra)e-r/2a

in which a is the Bohr radius and the subscript onΨ(r)gives the values of the quantum numbers n,l,ml. (a) PlotΨ(2002r)and show that your plot is consistent with the dot plot of Fig. 39-21. (b) Show analytically thatΨ(2002r)has a maximum at r=4a. (c) Find the radial probability densityP200(r)for this state. (d) Show that

∫0∞P200(r)dr=1

and thus that the expression above for the wave function Ψ200(r)has been properly normalized.

What are the (a) energy, (b) magnitude of the momentum, and (c) wavelength of the photon emitted when a hydrogen atom undergoes a transition from a state with n = 3 to a state with n = 1 ?

What is the ratio of the shortest wavelength of the Balmer series to the shortest wavelength of the Lyman series?

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 n=4?

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