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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: Starting with the assumption that a general wave function may be treated as an algebraic sum of sinusoidal functions of various wave numbers, explain concisely why there is an uncertainty principle.

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?

Generally speaking, why is the wave nature of matter so counterintuitive?

A beam of electrons strikes a crystal at an angleθwith the atomic planes, reflects of many atomic planes below the surface, and then passes into a detector also making angleθwith the atomic planes. (a) If the minimumθgiving constructive interference is.35° What is the ratioλ/d, Where is the spacing between atomic planes? (b) At what other angles, if any, would constructive interference occur?

A beam of electrons of 25 eVkinetic energy is directed at a single slip of 2.0 μm width, then detected at a screen 4m beyond the slit. How far from a point directly in the line of the beam is the first location where no electrons are ever detected?
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