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Wavelength questions

You are an engineer designing a switch that works by the photoelectric effect. The metal you wish to use in your device requires 6.7x10 (to the -19 power. J/atom to remove an electron. Will the switch work if the light falling on the metal has a wavlength of 540nm or greater? Why or why not?

Radiation in the ultraviolet region of the electromagnetic spectrum is quite entergetic. It is this radiation that causes dyes to fade and your skin to burn. If you are bombarded with 1.00 mol of photons with a wavelength of 375nm, what amount of energy (in kilojoules per mole of photons) are you being subjected to?

What is the shortest wavelength photon an excited H atom can emit? Explain briefly.

Solution Preview

All of your questions revolve around the photon theory of light, originally discovered by Max Planck in 1900 and expanded upon by Einstein in 1905. The crux of the theory is the fact that light can be modeled as a dicrete set of packets, called photons. Each packet carries a finite amount of energy which is specifed by the Planck relationship, which states:

Energy of a photon = Planck's Constant * frequency of light.

Thus the energy carried by light is directly proportional to its frequency. Therefore, blue light is more energetic than red light, because its frequency if higher. This idea immediately answers your first two questions if we also recall that the frequency of light, like any wave, is related to its wavelength by the equation:

frequency x wavelength = speed of the wave

or specificially for light:

frequency x wavelength = speed of light (which is 3.00 E 8 m/s)
(note the 3.00 E8 is my notation for 3.0 x 10^8)

In your first question your device needs 6.7E-19 J/atom to remove an electron from the atom. Where does this energy come from? It comes from a photon of light hitting the device and imparting its energy to it. Thus the energy of each photon hitting the ...

Solution Summary

The solution is given step-by-step in approximately 500 words.