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Chapter 8: Q13P (page 344)

The Frank Hertz experiment involved shooting electrons into a low density gas of mercury atoms and observing discrete amounts of kinetic energy loss by the electrons. Suppose that instead the similar experiment is done with a very cold gas of atomic hydrogen, so that all of the hydrogen atoms are initially in ground state. If the kinetic energy of an electron is 11.6 eV just before it collides with a hydrogen atom. How much kinetic energy will the electron have just after it collides with and excites the hydrogen atom?

Short Answer

Expert verified

The kinetic energy of electron after collision is1.4eV .

Step by step solution

01

Identification of given data

The kinetic energy of electron just before collision isKi=11.6eV

02

Conceptual Explanation

The electron loses it kinetic energy just after collision with atomic hydrogen and kinetic energy of electron just after collision will be equal to the difference between kinetic energy before collision and energy of hydrogen atom in first excited state.

03

Determination of kinetic energy of electron after collision

The kinetic energy of electron just after collision is given as:

Kf=Ki-Ee

Here, Ee is the energy of hydrogen in first excited state and its value is 10.2eV

Substitute all the values in the above equation.

Kf=11.6eV-10.2eVKf=1.4eV

Therefore, the kinetic energy of electron just after collision is 1.4eV.

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Most popular questions from this chapter

When starlight passes through a cold cloud of hydrogen gas, some hydrogen atoms absorb energy, then reradiate it in all directions. As a result, spectrum of the star shows dark absorption lines at the energies for which less energy from the star reaches us. How does the spectrum of dark absorption lines for very cold hydrogen differs from the spectrum of bright emission lines from very hot hydrogen?

Suppose that a collection of quantum harmonic oscillators occupies the lowest four energy levels, and the spacing between levels is 0.4 eV. What is the complete emission spectrum for this system? That is, what photon energies will appear in the emissions? Include all energies, whether or not they fall in the visible region of the electromagnetic spectrum.

Summarize the differences and similarities between different energy levels in a quantum oscillator. Specifically for the first two levels in figure 8.26, compare the angular frequency Ks/m, the amplitude , and the kinetic energyk at the same value of . ( In a quantum-mechanical analysis the concepts of angular frequency and amplitude require reinterpretation. Nevertheless, there remain elements of the classical picture. For example, larger amplitude corresponds to a higher probability of observing a large stretch.)


Assume that a hypothetical object has just four quantum states, with the following energies:

-1.0eV(third excited state)

-1.8eV(second excited state)

-2.9eV(first excited state)

-4.8eV(ground state)

(a) Suppose that material containing many such objects is hit with a beam of energetic electrons, which ensures that there are always some objects in all of these states. What are the six energies of photons that could be strongly emitted by the material? (In actual quantum objects there are often “selection rules” that forbid certain emissions even though there is enough energy; assume that there are no such restrictions here.) List the photon emission energies. (b) Next, suppose that the beam of electrons is shut off so that all of the objects are in the ground state almost all the time. If electromagnetic radiation with a wide range of energies is passed through the material, what will be the three energies of photons corresponding to missing (“dark”) lines in the spectrum? Remember that there is hardly any absorption from excited states, because emission from an excited state happens very quickly, so there is never a significant number of objects in an excited state. Assume that the detector is sensitive to a wide range of photon energies, not just energies in the visible region. List the dark-line energies.

A certain material is kept at very low temperature. It is observed that when photons with energies between 0.2 and 0.9 eV strike the material, only photons of 0.4 eV and 0.7 eV are absorbed. Next, the material is warmed up so that it starts to emit photons. When it has been warmed up enough that 0.7 eV photons begin to be emitted, what other photon energies are also observed to be emitted by the material? Explain briefly.
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