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Chapter 8: Q12P (page 344)

N=1 is the lowest electronic energy state for a hydrogen atom. (a) If a hydrogen atom is in a state N=4, what is K+U for this atom (in eV)? (b) The hydrogen atom makes a transition to state N=2, Now what is K+U in electron volts for this atom? (c) What is energy (in eV) of the photon emitted in the transition from level N=4 to N=2? (d) Which of the arrows in figure 8.40 represents this transition?

Short Answer

Expert verified

The total energy level in the fourth level is -0.85eV.

Step by step solution

01

Identification of given data

The state of hydrogen atom is N=4

02

Conceptual Explanation

The energy of an atom at a particular level varies with the level of the atom. The energy in the lowest level of hydrogen atom is 13.6 eV.

03

Determination of total energy of hydrogen atom

The total energy of hydrogen atom is given as:

K+UN=-13.6eVN2

Substitute all the values in the above equation.

K+U4=-13.6eV42K+U4=-0.85eV

Therefore, the total energy of hydrogen is -0.85eV

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Most popular questions from this chapter

A hot bar of iron glows a dull red. Using our simple ball-spring model of a solid (Figure 8.23), answer the following questions,explaining in detail the processes involved. You will need to make some rough estimates of atomic properties based on prior work. (a) What is the approximate energy of the lowest-energy spectral emission line? Give a numerical value. (b) What is the approximate energy of the highest-energy spectral emission line? Give a numerical value. (c) What is the quantum number of the highest-energy occupied state? (d) Predict the energies of two other lines in the emission spectrum of the glowing iron bar. (Note: Our simple model is too simple-the actual spectrum is more complicated. However, this simple analysis gets at some important aspects of the phenomenon.)

Suppose we have a reason to suspect that a certain quantum object has only three quantum states.When we excite a collection of such objects we observe that they emit electromagnetic radiation of three different energies: 0.3 eV(infrared), 2.0 eV(visible), and 2.3 eV(visible).

(a) Draw a possible energy-level diagram for one of the quantum objects, which has three bound states. On the diagram, indicate the transitions corresponding to the emitted photons, and check that the possible transitions produce the observed photons and no others. The energyK+U of the ground state is -4eV. Label the energies of each level ( K+U, which is negative).

(b) The material is now cooled down to a very low temperature, and the photon detector stops detecting photon emissions. Next a beam of light with a continuous range of energies from infrared through ultraviolet shines on the material, and the photon detector observes the beam of light after it passes through the material. What photon energies in this beam of light are observed to be significantly reduced in intensity ("dark absorption lines")? Energy of highest-energy dark line: eV Energy of lowest-energy dark line: eV

(c) There exists another possible set of energy levels for these objects which produces the same photon emission spectrum. On an alternative energy-level diagram, different from the one you drew in part (a), indicate the transitions corresponding to the emitted photons, and check that the possible transitions produce the observed photons and no others. When you are sure that your alternative energy-level diagram is consistent with the observed photon energies, enter the energies of each level (K+U, which is negative).

(d) For your second proposed energy-level scheme, what photon energies would be observed to be significantly reduced in intensity in an absorption experiment ("dark absorption lines")? (Given the differences from part (b), you can see that an absorption measurement can be used to tell which of your two energy-level schemes is correct).

At t =0 all of the atoms in a collection of 10000 atoms are in a excited state whose lifetime is 25 ns. Approximately how many atoms will still be in excited state at t= 12 ns.

If you double the amplitude, what happens to the frequency in a classical (non quantum) harmonic oscillator? In a quantum harmonic oscillator?

Some material consisting of a collection of microscopic objects is kept at a high temperature. A photon detector capable of detecting photon energies from infrared through ultraviolet observes photons emitted with energies of0.3eV,0.5eV,0.8eV,2,0eV,2.5eV,and2.8eV. These are the only photon energies observed. (a) Draw and label a possible energy-level diagram for one of the microscopic objects, which has four bound states. On the diagram, indicate the transitions corresponding to the emitted photons. Explain briefly. (b) Would a spring–mass model be a good model for these microscopic objects? Why or why not? (c) The material is now cooled down to a very low temperature, and the photon detector stops detecting photon emissions. Next, a beam of light with a continuous range of energies from infrared through ultraviolet shines on the material, and the photon detector observes the beam of light after it passes through the material. What photon energies in this beam of light are observed to be significantly reduced in intensity (“dark absorption lines”)? Explain briefly.
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