Figure 39-29 a shows a thin tube in which a finite potential trap has been set up where . An electron is shown travelling rightward toward the trap, in a region with a voltage of , where it has a kinetic energy of 2.00 eV. When the electron enters the trap region, it can become trapped if it gets rid of enough energy by emitting a photon. The energy levels of the electron within the trap are , and , and the non quantized region begins at as shown in the energylevel diagram of Fig. 39-29b. What is the smallest energy such a photon can have?
The energy of the photon is 7eV.
An electron is shown travelling rightward toward the trap, in a region with a voltage , where it has a kinetic energy of .
The electron losses some energy when it jumps from the quantized region to the non-quantized region. The energy of the photon is the sum of the kinetic energy and the potential energy, the potential energy is equal to the difference between the third and fourth levels.
The kinetic energy is 2 eV therefore, the energy of the photon is,
Since, the change in energy is equal to .
Substitute for in the above equation.
Substitute 2 eV for K, for role="math" localid="1661767190577" and 4 eV for in the above equation.
Hence, the energy of the photon is 7 eV.
A hydrogen atom can be considered as having a central point- like proton of positive charge e and an electron of negative charge -e that is distributed about the proton according to the volume charge density . Here is a constant, , and r is the distance from the center of the atom.
(a) Using the fact that the hydrogen is electrically neutral, find A . the
(b) Then find magnitude
(c) Then find direction of the atom’s electric field at .
An electron is trapped in a one-dimensional infinite potential well that is 100 pm wide; the electron is in its ground state. What is the probability that you can detect the electron in an interval of width centered at x = (a) 25 pm, (b) 50 pm, and (c) 90 pm? (Hint: The interval x is so narrow that you can take the probability density to be constant within it.)
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