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Chapter 8: Q2Q (page 343)

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?

Short Answer

Expert verified

Hydrogen gas with a lower temperature will absorb more photons than hydrogen gas with a higher temperature.

Step by step solution

01

Concept Introduction

Whenever the bright lines fall on the metal surface, the emission of a photon takes place, and when the dark lines fall on the metal surface, the absorption of a photon takes place.

02

Explanation

In the case of cold hydrogen gas, at the initial stage, most of the electrons are in the ground state, due to which resultant photons have higher energy because of the difference of energy from the ground state to a first excited state.

Whereas, in the case of hot hydrogen gas, most of the electrons are in the excited state at the initial stage, resulting in lower energy because of the difference of energy from the ground state to the first excited state.

Therefore hydrogen gas with a lower temperature will absorb more photons than hydrogen gas with a higher temperature.

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Most popular questions from this chapter

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鈥搈ass 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 (鈥渄ark absorption lines鈥�)? Explain briefly.


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 鈥渟election rules鈥� 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 (鈥渄ark鈥�) 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.

Suppose that a collection of quantum harmonic oscillators occupies the lowest four energy levels, and the spacing between levels is 0.4鈥�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.

Consider a microscopic spring鈥搈ass system whose spring stiffness is50N/m, and the mass is4脳10-26kg. (a) What is the smallest amount of vibrational energy that can be added to this system? (b) What is the difference in mass (if any) of the microscopic oscillator between being in the ground state and being in the first excited state? (c) In a collection of these microscopic oscillators, the temperature is high enough that the ground state and the first three excited states are occupied. What are possible energies of photons emitted by these oscillators?

If you try to increase the energy of a quantum harmonics oscillator by adding an amount of energy 12hks/m, the energy doesn鈥檛 increase. Why not?

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