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Ch.7 - Quantum-Mechanical Model of the Atom
Tro - Chemistry: A Molecular Approach 4th Edition
Tro4th EditionChemistry: A Molecular ApproachISBN: 9780134112831Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoTro 4th EditionCh.7 - Quantum-Mechanical Model of the AtomProblema 91
Capitolo 7, Problema 91

A laser produces 20.0 mW of red light. In 1.00 hr, the laser emits 2.29×1020 photons. What is the wavelength of the laser?

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Identify the given values: Power (P) = 20.0 mW, Time (t) = 1.00 hr, Number of photons (N) = 2.29 \(\times\) 10^{20}.
Convert the power from milliwatts to watts: 1 mW = 0.001 W, so 20.0 mW = 0.020 W.
Convert the time from hours to seconds: 1 hr = 3600 s, so 1.00 hr = 3600 s.
Calculate the total energy emitted by the laser using the formula: Energy (E) = Power (P) \(\times\) Time (t).
Use the energy of a single photon formula: E_{photon} = \(\frac{E}{N}\), and relate it to wavelength using E_{photon} = \(\frac{hc}{\lambda}\), where h is Planck's constant and c is the speed of light, to solve for the wavelength \(\lambda\).

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Photon Energy

The energy of a photon is given by the equation E = hν, where E is energy, h is Planck's constant (6.626 x 10^-34 J·s), and ν (nu) is the frequency of the light. The frequency can be related to the wavelength (λ) using the equation c = λν, where c is the speed of light (approximately 3.00 x 10^8 m/s). Understanding photon energy is essential for calculating the wavelength from the number of emitted photons.
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Photon Energy Formulas

Power and Energy Relationship

Power is defined as the rate at which energy is emitted or transferred. In this context, the laser's power output (20.0 mW) indicates how much energy is emitted per unit time. To find the total energy emitted over a specific time period, you can multiply the power by the time (in seconds). This relationship is crucial for determining the total energy associated with the emitted photons.
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Power and Root Functions Example

Wavelength Calculation

Wavelength can be calculated using the relationship between energy and frequency. Once the total energy emitted by the laser is determined, the energy per photon can be found by dividing the total energy by the number of photons emitted. This energy can then be used to find the wavelength using the equation λ = hc/E, where E is the energy per photon. This process is key to solving the question regarding the wavelength of the laser light.
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Frequency-Wavelength Relationship
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