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Chapter 6: Problem 63

A carbon dioxide laser produces radiation of wavelength \(10.6\) micrometers (1 micrometer \(=10^{-6}\) meter). If the laser produces about one joule of energy per pulse, how many photons are produced per pulse?

Short Answer

Expert verified
Answer: Approximately 5.34 × 10^{18} photons are produced per pulse.

Step by step solution

01

Calculate the energy of a single photon

First, let's calculate the energy of a single photon using the given wavelength and the formula E = h * c / λ. We have: - h (Planck's constant) = 6.626 × 10^{-34} J·s - c (speed of light) = 3.0 × 10^8 m/s - λ (wavelength) = 10.6 × 10^{-6} m (converting from micrometers to meters) Using these values, we can calculate the energy of a single photon: E = (6.626 × 10^{-34} J·s) * (3.0 × 10^8 m/s) / (10.6 × 10^{-6} m).
02

Evaluate the energy of a single photon

Now, let's evaluate the energy of a single photon using the values from the previous step: E = (6.626 × 10^{-34} J·s) * (3.0 × 10^8 m/s) / (10.6 × 10^{-6} m) = 1.874 × 10^{-19} J The energy of a single photon is 1.874 × 10^{-19} Joules.
03

Calculate the number of photons produced per pulse

We are given that the laser produces about one Joule of energy per pulse. To find the number of photons produced in each pulse, we can divide the total energy per pulse by the energy of a single photon: Number of photons = (Total energy per pulse) / (Energy of a single photon) = 1 J / (1.874 × 10^{-19} J).
04

Evaluate the number of photons produced per pulse

Finally, let's evaluate the number of photons produced per pulse: Number of photons = 1 J / (1.874 × 10^{-19} J) = 5.34 × 10^{18} Approximately 5.34 × 10^{18} photons are produced per pulse by the carbon dioxide laser.

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