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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鈭�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鈫�3 , 4鈫�2,4鈫�1 ,3鈫�2 ,3鈫�1 and2鈫�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

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.

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?

The mean lifetime of a certain excited atomic state is 5 ns. What is the probability of the atom staying in this excited state for t=10 ns or more?

For a certain diatomic molecule, the lowest-energy photon observed in the vibrational spectrum is 0.17eV. What is the energy of a photon emitted in a transition from the 5th excited vibrational energy level to the 2nd excited vibrational energy level, assuming no change in the rotational energy?

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.)
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