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Chapter 5: Q4CQ (page 185)

Explain to your friend, who is skeptical about energy quantization, the simple evidence provided by distinct colors you see when you hold a CD (serving as grating) near a fluorescent light. It may be helpful to contrast this evidence with the spectrum produced by an incandescent light, which relies on heating to produce a rather nonspecific blackbody spectrum.

Short Answer

Expert verified

The discrete colors seen when you look at a CD are a direct evidence of energy quantization because the color of light that we see depends on its wavelength, which is related to its energy. If the energy is quantized, the wavelengths of the light are discrete so we see discrete colors (not white light as in case of a light bulb).

Step by step solution

01

Given data

If E is discrete, wavelength is discrete.

02

 Step 2: Concept of wavelength of electromagnetic radiation

The wavelength of an electromagnetic radiation is related to its energy by relation:

E=hc位

Where, his the Planck's constant, cis the speed of light,位is the wavelength and Eis the energy.

03

Diffraction of light

A CD has tiny grooves on it. Based on the size of the grooves, certain wavelengths of the light are diffracted by the CD in different directions. A fluorescent light source emits only certain wavelengths. So, when we look at a CD, illuminated by a fluorescent light source, we see only the wavelength that is diffracted at an angle towards our eye. If the wavelengths were not discrete, we would see multiple wavelengths at a time from the same spot on the CD resulting in white color.

04

Incandescent light source

You don't see colors when you illuminate the CD by an incandescent light source. This is because, the wavelengths emitted by an incandescent light source are not discrete, they are continuous and their intensity depends on the temperature of the heating filament. Continuous means all wavelengths are present. You cannot say that this particular wavelength is absent in this incandescent light source.

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Most popular questions from this chapter

We say that the ground state for the particle in a box has nonzero energy. What goes wrong with 唯in equation 5.16 if n = 0 ?

Simple models are very useful. Consider the twin finite wells shown in the figure, at First with a tiny separation. Then with increasingly distant separations, In all case, the four lowest allowed wave functions are planned on axes proportional to their energies. We see that they pass through the classically forbidden region between the wells, and we also see a trend. When the wells are very close, the four functions and energies are what we might expect of a single finite well, but as they move apart, pairs of functions converge to intermediate energies.

(a) The energies of the second and fourth states decrease. Based on changing wavelength alone, argue that is reasonable.

(b) The energies of the first and third states increase. Why? (Hint: Study bow the behaviour required in the classically forbidden region affects these two relative to the others.)

(c) The distant wells case might represent two distant atoms. If each atom had one electron, what advantage is there in bringing the atoms closer to form a molecule? (Note: Two electrons can have the same wave function.)

Consider a particle of mass mand energy E in a region where the potential energy is constant U0. Greater than E and the region extends tox=+鈭�

(a) Guess a physically acceptable solution of the Schrodinger equation in this region and demonstrate that it is solution,

(b) The region noted in part extends from x = + 1 nm to +鈭�. To the left of x = 1nm. The particle鈥檚 wave function is Dcos (109m-1 x). Is also greater than Ehere?

(c) The particle鈥檚 mass m is 10-3 kg. By how much (in eV) doesthe potential energy prevailing from x=1 nm to U0. Exceed the particle鈥檚 energy?

A student of classical physics says, "A charged particle. like an electron orbiting in a simple atom. shouldn't have only certain stable energies: in fact, it should lose energy by electromagnetic radiation until the atom collapses." Answer these two complaints qualitatively. appealing to as few fundamental claims of quantum mechanics as possible.

When is the temporal part of the wave function 0 ? Why is this important?
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