A 200-W infrared laser emits photons with a wavelength of 2.0 ×10^-6 m while a 200-W ultraviole

step 1 For this exercise, we have two lasers, one infrared whose wavelength is 2 times 10 to the minus

A 200-W infrared laser emits photons with a wavelength of...

A 200-W infrared laser emits photons with a wavelength of $2.0 \times 10^{-6} \mathrm{~m}$ while a 200-W ultraviolet light emits photons with a wavelength of $7.0 \times 10^{-8} \mathrm{~m}$. (a) Which has greater energy, a single infrared photon or a single ultraviolet photon? (b) What is the energy of a single infrared photon and the energy of a single ultraviolet photon? (c) How many photons of each kind are emitted per second?

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Key Concepts

Planck's Relation

This concept states that the energy of a photon is directly proportional to its frequency and inversely proportional to its wavelength, as described by the equation E = hc/?, where h is Planck's constant and c is the speed of light. It forms the basis for calculating the energy carried by individual photons in electromagnetic radiation.

Inverse Proportionality of Wavelength and Photon Energy

This principle tells us that shorter wavelengths correspond to higher photon energies. It is critical for comparing photons from different parts of the electromagnetic spectrum, such as infrared versus ultraviolet light, emphasizing that even if the total power is the same, the energy per photon can vary with the wavelength.

Photon Flux and Power Relationship

This concept connects the total power of a light source to the number of photons it emits per second. Since power is the energy delivered per unit time, dividing the source's power by the energy per photon (derived from Planck's relation) yields the photon flux, which is essential in understanding how many photons are produced in a light emission process.

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