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How many photons per second are emitted by a \(7.50-\mathrm{mW}\) \(\mathrm{CO}_{2}\) laser that has a wavelength of 10.6\(\mu \mathrm{m} ?\)

Short Answer

Expert verified
Approximately 2.33 × 10^{16} photons/second.

Step by step solution

01

Calculate Energy of a Single Photon

The energy of a single photon can be found using the formula \( E = \frac{hc}{\lambda} \), where \( h \) is Planck's constant \( 6.626 \times 10^{-34} \text{ Js} \), \( c \) is the speed of light \( 3.00 \times 10^{8} \text{ m/s} \), and \( \lambda \) is the wavelength \( 10.6 \times 10^{-6} \text{ m} \). Substituting these values into the formula: \[ E = \frac{6.626 \times 10^{-34} \times 3.00 \times 10^{8}}{10.6 \times 10^{-6}} \text{ J}. \]
02

Calculate Photons Emitted Per Second

The number of photons emitted per second is given by \( N = \frac{P}{E} \), where \( P \) is the power of the laser. The power given is \( 7.50 \mathrm{mW} = 7.50 \times 10^{-3} \text{ W} \). Using the energy calculated in Step 1, substitute into the formula: \[ N = \frac{7.50 \times 10^{-3}}{E} \text{ photons per second}, \] where \( E \) is the energy found in Step 1.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

CO2 Laser
A CO2 laser is a type of gas laser, where the medium is composed of carbon dioxide, along with other gases like nitrogen and helium. It operates primarily in the infrared region of the electromagnetic spectrum, with a typical wavelength of 10.6 micrometers. This makes it invisible to the human eye.
  • Due to its wavelength, it is ideal for industrial applications such as cutting, welding, and engraving.
  • CO2 lasers are highly efficient with a high power output, making them particularly useful in medical and military fields as well.
The mechanism of photon emission in CO2 lasers involves exciting nitrogen molecules, which then transfer energy to carbon dioxide molecules, creating a cascade of amplifiable light through stimulated emission.
It relies heavily on the properties of molecules involved and requires precise control over several parameters to work effectively.
Electromagnetic Spectrum
The electromagnetic spectrum encompasses all types of electromagnetic radiation, from gamma rays, with the shortest wavelengths, to radio waves with the longest. Infrared, which is the region that includes the output from a CO2 laser, covers wavelengths from about 700 nm to 1 mm.

Within this spectrum, different types of radiation are classified based on their wavelength and energy. For instance, ultraviolet light has shorter wavelengths and higher energy compared to visible light, whereas radio waves have longer wavelengths and lower energy.
  • Each portion of the spectrum has unique properties and interactions with matter, which is why different portions are used for varied applications, from medical imaging to communication technology.
  • Understanding the spectrum allows for the development of technologies that utilize specific wavelengths for particular purposes.
Thus, knowing about the electromagnetic spectrum can help predict how different types of radiation interact with objects and organisms, enabling advancements in various scientific domains.
Planck's Constant
Planck's constant is a fundamental physical constant that plays a critical role in the field of quantum mechanics. Its value, approximately \(6.626 \times 10^{-34} \text{ Js}\), is used to quantify the size of quantum effects.
  • It relates the energy of a photon to its frequency through the equation \(E = h u\), where \(E\) is the energy, \(h\) is Planck's constant, and \(u\) is the frequency of the photon.
  • Planck’s constant was first introduced by Max Planck in 1900 and represents the smallest action or quantum of action in quantum mechanics.
This constant helps explain phenomena that classical physics cannot, such as the discrete nature of the energy levels in an atom or the particle-like behavior of light.
It's essential for the calculation of phenomena like photoelectric effect, emission spectra, and more, thereby serving as a cornerstone for theories and applications that define modern physics.

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Most popular questions from this chapter

(a) A nonrelativistic free particle with mass \(m\) has kinetic energy \(K .\) Derive an expression for the de Broglie wavelength of the particle in terms of \(m\) and \(K .\) (b) What is the de Broglie wavelength of an 800 -eV electron?

Light from an ideal spherical blackbody 15.0 \(\mathrm{cm}\) in diameter is analyzed using a diffraction grating having 3850 lines/cm. When you shine this light through the grating, you observe that the peak-intensity wavelength forms a first-order bright fringe at \(\pm 11.6^{\circ}\) from the central bright fringe. (a) What is the temperature of the blackbody? (b) How long will it take this sphere to radiate 12.0 \(\mathrm{MJ}\) of energy?

(a) The uncertainty in the \(y\) -component of a proton's position is \(2.0 \times 10^{-12} \mathrm{m} .\) What is the minimum uncertainty in a simultaneous measurement of the \(y\) -component of the proton's velocity? (b) The uncertainty in the \(z\) -component of an electron's velocity is 0.250 \(\mathrm{m} / \mathrm{s}\) . What is the minimum uncertainty in a simultaneous measurement of the \(z\) -coordinate of the electron?

An atom with mass \(m\) emits a photon of wavelength \(\lambda\) . (a) What is the recoil speed of the atom? (b) What is the kinetic energy \(K\) of the recoiling atom? (c) Find the ratio \(K / E,\) where \(E\) is the energy of the emitted photon. If this ratio is much less than unity, the recoil of the atom can be neglected in the emission process. Is the recoil of the atom more important for small or large atomic masses? For long or short wavelengths? (d) Calculate \(K\) (in electron volts) and \(K / E\) for a hydrogen atom (mass \(1.67 \times\) \(10^{-27} \mathrm{kg} )\) that emits an ultraviolet photon of energy 10.2 eV. Is recoil an important consideration in this emission process?

A pesky 1.5-mg mosquito is annoying you as you attempt to study physics in your room, which is 5.0 m wide and 2.5 \(\mathrm{m}\) high. You decide to swat the bothersome insect as it flies toward you, but you need to estimate its speed to make a successful hit. (a) What is the maximum uncertainty in the horizontal position of the mosquito? (b) What limit does the Heisenberg uncertainty principle place on your ability to know the horizontal velocity of this mosquito? Is this limitation a serious impediment to your attempt to swat it?

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