Removing Birthmarks. Pulsed dye lasers emit light of...

Removing Birthmarks. Pulsed dye lasers emit light of wavelength 585 nm in 0.45 -ms pulses to remove skin blemishes such as birthmarks. The beam is usually focused onto a circular spot 5.0 $\mathrm{mm}$ in diameter. Suppose that the output of one such laser is 20.0 $\mathrm{W}$ . (a) What is the energy of each photon, in eV? (b) How many photons per square millimeter are delivered to the blemish during each pulse?

Key Concepts

Photon Energy Calculation

This concept involves calculating the energy of a single photon using the relationship E = hc/?, where h is Planck’s constant, c is the speed of light, and ? is the wavelength of the light. It is fundamental in quantum mechanics and photonics, as it connects the energy of light with its wavelength.

Energy Unit Conversion

In many physics problems, it is necessary to convert between different units of energy. In the context of photon energy, once the energy is determined in joules, it is often converted to electron volts (eV) using the conversion factor 1 eV = 1.602×10?¹? joules. This conversion is essential for comparing energy scales in atomic and molecular physics.

Laser Pulse Energy Determination

A laser beam’s power and the duration of its pulse determine the total energy delivered in a single pulse. This energy can be calculated by multiplying the output power (in watts, which equals joules per second) by the pulse duration. This concept is key in applications where controlled energy delivery, such as in medical or industrial lasers, is necessary.

Area Computation for Circular Beam Spots

When a beam is focused onto a spot, the area over which the energy is distributed must be calculated to understand the energy density. For a circular spot, the area is determined by the formula A = ?(d/2)², where d is the diameter. This is critical for assessing the intensity or fluence (energy per unit area) delivered by the laser.

Photon Flux and Energy Density

Once the energy per pulse and the energy per photon are known, the total number of photons can be obtained. Dividing this number by the area of the beam spot gives the photon flux, or the number of photons per unit area. This concept is important in understanding how light interacts with materials, particularly in precision applications such as laser treatment or photochemical reactions.

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