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Chapter 10: Q43E (page 469)

Question: From the qualitative shapes of the interatomic potential energies in Fig. 10.21, would you expect the vibrational level in the excited electronic state to be spaced the same. Farther apart, or closer together than those in the lower energy electronic state? Explain what about the rotational levels?

Short Answer

Expert verified

Answer

  1. Due to the smaller value of fractionκμ, the vibrational levels will be closely packed. As The minima for rotational levels are located at larger separation, thus, the levels are more closely packed due to increased rotational inertia

Step by step solution

01

Concept of interatomic potential energy.

The energy contributed to the total energy of the solid, due to the interactions that take place between the atom of a single molecule or atoms of adjacent molecules is called interatomic potential energy. the interatomic forces can be attractive as well as repulsive.

02

Explanation

Due to the smaller curvature of excited state potential energy, it affects the spring constant. In this case the fraction κμwould have smaller values, hence, the vibrational levels would be closely placed.

For the excited curves, their minima are located at a larger separation. This increases the rotational inertia hence the rotational energy levels are more closely packed.

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Most popular questions from this chapter

Question: Referring to equations(10-2), lobe I of the hybrid states combines the spherically symmetric s state with the state that is oriented along thez-axis. and thus sticks out in the direction (see Exercises 28 and 33), If Figure is a true picture, then in a coordinate system rotated counterclockwise about they-axis by the tetrahedral angle, lobe II should become lobe. In the new frame. -values are unaffected. but what had been values in the 2x -plane become values in the -plane. according tox=x'cosα+z'sinα and z'cosα-x'sinα, whereα=109.5o iscos-1(-13) , or .

(a) Show that lobe II becomes lobe I. Note that since neither the 2s state nor the radial part of the p states is affected by a rotation. only the angular parts given in equations (10-1) need be considered.

(b) Show that if lobe II is instead rotated about thez-axis by simply shifting φby±1200 . it becomes lobes III and IV.

The bond length of theN2 molecule is0.11 nm , and its effective spring constant is 2.3×103N/mat room temperature.

(a) What would be the ratio of molecules with rotational quantum numberℓ=1 to those withℓ=0 (at the same vibrational level), and

(b) What would be the ratio of molecules with vibrational quantum numbern=1 to those with n=0(with the same rotational energy)?

The diagram shows a bridge rectifier circuit. A sinusoidal input voltage is fed into four identical diodes. each represented by the standard diode circuit symbol. The symbol indicates the direction of conventional current flow through the diode. The plots show input and output voltages versus time. Note that the output voltage is strictly in one direction. Explain

(a) how this circuit produces the unidirectional output voltage it does, and

(b) what features in the output plot indicate that the band gap of the diodes is about half an electronvolt, (It might seem that about one volt is correct, but consider how many diodes are on and in series at any given instant. In fact, although not the usual habit, it might be more accurate to plot the output voltage shifted upward relative to the input.)

Question:If electrical conductivity were determined by the mere static presence of positive ions rather than by their motion the collision time would be inversely proportional to the electron's average speed. If however, it were dominated by the motion of the ions, it should be inversely proportional to the “area" presented by a jiggling ion, which is in turn proportional to the square of its amplitude as an oscillator. Argue that only the latter view gives the correct temperature dependence in conductors of σ∝T-1. Use the equipartition theorem (usually covered in introductory thermodynamics and also discussed in Section 9.9).

Starting with equation (10-4), show that if Δn is-1 as a photon is emitted by a diatomic molecule in a transition among rotation-vibration states, but Δℓcan be±1 . Then the allowed photon energies obey equation (10-6).
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