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Chapter 4: Q5CQ (page 133)

Question: Incandescent lightbulbs heat up a filament “white hot,” producing light of all wavelengths that has little to do with the filament’s composition. Gas vapor bulbs, such as sodium and mercury streetlights, produce colors that do depend on the gas in the bulb. Viewed with a diffraction grating (even a simple CD!), whereas the incandescent spectrum is continuous, that of a gas vapor (or fluorescent) bulb has characteristic lines. How is this indirect evidence of the wave nature of orbiting electrons?

Short Answer

Expert verified

Answer:

Only specific quantized energies are allowed for orbiting electrons, which leads to only specific wavelengths of photons. The electron should act like a wave inside the tiny constraints of the atom, creating quantized standing waves.

Step by step solution

01

The wavelength of a particle 

The wavelength of a particle can be obtained using the formula λ=hp=hmv.

02

Explanation

Gas vapor filaments, like sodium, form distinctive lines, or lines with particular wavelengths or energy. This indicates that, in accordance with the energy conservation principle, electrons either make the same transition across energy levels or exist in quantized states.

Bohr offered the theory that electrons behave as a wave that is contained in an orbit around the nucleus as one explanation. In accordance with this, some wavelengths (standing waves) can fit within these circles, much as how sound waves can fit inside of closed pipes or other musical instruments.

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Most popular questions from this chapter

Question: Atoms in a crystal form atomic planes at many different angles with respect to the surface. The accompanying figure shows the behaviors of representative incident and scattered waves in the Davisson-Germer experiment. A beam of electrons accelerated through 54 V is directed normally at a nickel surface, and strong reflection is detected only at an angle ϕof 500.Using the Bragg law, show that this implies a spacing D of nickel atoms on the surface in agreement with the known value of 0.22 nm.

In Example 4.2. neither|Ψ|2nor|Ψ|are given units—only proportionalities are used. Here we verify that the results are unaffected. The actual values given in the example are particle detection rates, in particles/second, ors-1. For this quantity, let us use the symbol R. It is true that the particle detection rate and the probability density will be proportional, so we may write|Ψ|2= bR, where b is the proportionality constant. (b) What must be the units of b? (b) What is|ΨT|at the center detector (interference maximum) in terms of the example’s given detection rate and b? (c) What would be|Ψ1|,|Ψ1|2, and the detection rate R at the center detector with one of the slits blocked?

The setup depicted in Figure4.6is used in a diffraction experiment using X-rays of0.26 nmwavelength. Constructive interference is noticed at angles of23.0oand,51.4obut none between. What is the spacingdof atomic planes?

The Moon orbits Earth at a radius of 3.84×108m. To do so as a classical particle. Its wavelength should be small. But small relative to what? Being a rough measure of the region where it is confined, the orbit radius is certainly a relevant dimension against which to compare the wavelength. Compare the two. Does the Moon indeed orbit as a classical particle? (localid="1659095974931" mEarth=5.98×1024kgand mmoon=7.35×1022kg)

All other things being equal, which would be more likely to exhibit its wave nature—a proton or an electron—and why? By making something unequal, how could you “compensate,” so as to make one as wavelike as the other?
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