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Chapter 8: Q3CP (page 331)

How many different photon energies would emerge from a collection of hydrogen atoms that occupy the lowest four energy states (N=1,2,3,4) ? (You need not calculate the energies of each states.

Short Answer

Expert verified

The six different photon energies would emerge from a collection of hydrogen atoms that occupy the lowest four energy states(N=1,2,3,4) .

Step by step solution

01

Understanding the concept

If the hydrogen atom gets drop from higher energy state to lower then it will emit a photon with energy equal to Ef−Ei.

Here Efis the energy of g hydrogen atom at higher level and Ei is the energy of hydrogen atom at lower level.

02

Calculate the number of different photon energies.

Draw the energy transition diagram of hydrogen atoms

From the above diagram it is clear that the six different photon energies, corresponding to transitions4→3 , 4→2,4→1 ,3→2 ,3→1 and2→1 are emerged.

Therefore six different photon energies would emerge from a collection of hydrogen atoms that occupy the lowest four energy states (N=1,2,3,4).

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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.)

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

What is the energy of the photon emitted by the harmonic oscillator with stiffness ks and mass m when it drops from energy level 5 to energy level 2?

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).

The first excited state of a mercury atom is 4.9eV above the ground state. A moving electron collides with a mercury atom and excites the mercury atom to its first excited state. Immediately after the collision the kinetic energy of the electron is 0.3eV. What was the kinetic energy of the electron just before the collision?
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