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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.)

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.

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?

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.)

Make a rough estimate of this uniform energy spacing in electron volts (where 1 eV=1.6×10−19 J). You will need to make some rough estimates of atomic properties based on prior work. For comparison with the spacing of these vibrational energy states, note that the spacing between quantized energy levels for "electronic" states such as in atomic hydrogen is of the order of several electron volts.

(b) List several photon energies that would be emitted if a number of these vibrational energy levels were occupied due to collisional excitation. To what region of the spectrum (x-ray, visible, microwave, etc.) do these photons belong? (See Figure 8.1 at the beginning of the chapter.)

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