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Chapter 4: Problem 11

The distance between atoms in a molecule is about \(10^{-8} \mathrm{cm} .\) Can visible light be used to "see" molecules?

Short Answer

Expert verified
No, visible light cannot be used to 'see' molecules because the wavelength of visible light is larger than the distance between atoms in a molecule, thereby exceeding the resolution limit.

Step by step solution

01

Determine the Range of Visible Light Wavelength

Visible light has a wavelength range from approximately \(4 \times 10^{-5} cm\) to \(7 \times 10^{-5} cm\).
02

Compare the Resolution with the Molecular Distance

The given distance between atoms in a molecule is \(10^{-8} cm\), which is far less than the wavelength range of visible light.
03

Draw the Conclusion

Given that the size of an object must be approximately the same as or larger than the wavelength of the light used to see it, the molecule, with its atomic distance of \(10^{-8} cm\), is smaller than the wavelength of visible light. Consequently, it is not possible to 'see' molecules by using visible light as its resolution is much lower than the distance between atoms in a molecule.

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Most popular questions from this chapter

A single slit of width 0.1 mm is illuminated by a mercury light of wavelength 576 nm. Find the intensity at a \(10^{\circ}\) angle to the axis in terms of the intensity of the central maximum.

Two slits of width \(2 \mu \mathrm{m},\) each in an opaque material, are separated by a center-to-center distance of \(6 \mu \mathrm{m}\). A monochromatic light of wavelength \(450 \mathrm{nm}\) is incident on the double- slit. One finds a combined interference and diffraction pattern on the screen. (a) How many peaks of the interference will be observed in the central maximum of the diffraction pattem? (b) How many peaks of the interference will be observed if the slit width is doubled while keeping the distance between the slits same? (c) How many peaks of interference will be observed if the slits are separated by twice the distance, that is, \(12 \mu \mathrm{m}\), while keeping the widths of the slits same? (d) What will happen in (a) if instead of 450-nm light another light of wavelength \(680 \mathrm{nm}\) is used? (e) What is the value of the ratio of the intensity of the central peak to the intensity of the next bright peak in (a)? (f) Does this ratio depend on the wavelength of the light? (g) Does this ratio depend on the width or separation of the slits?

An amateur astronomer wants to build a telescope with a diffraction limit that will allow him to see if there are people on the moons of Jupiter. (a) What diameter mirror is needed to be able to see \(1.00-\mathrm{m}\) detail on a Jovian moon at a distance of \(7.50 \times 10^{8} \mathrm{km}\) from Earth? The wavelength of light averages \(600 \mathrm{nm}\). (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?

Show that a diffraction grating cannot produce a second-order maximum for a given wavelength of light unless the first-order maximum is at an angle less than \(30.0^{\circ}\)

How many complete orders of the visible spectrum \((400 \mathrm{nm}<\lambda<700 \mathrm{nm})\) can be produced with a diffraction grating that contains 5000 lines per centimeter?
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