The watt is the derived SI unit of power, the measure of energy per unit time: 1 W=1 J/s. A semiconductor laser in a CD player has an output wavelength of 780 nm and a power level of 0.10 mW. How many photons strike the CD surface during the playing of a CD 69 minutes in length?

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Convert the power from milliwatts to watts by using the conversion factor: 1 mW = 0.001 W.

Calculate the total energy output by the laser over 69 minutes by multiplying the power (in watts) by the time (in seconds). Remember to convert minutes to seconds.

Use the energy of a single photon formula, E = \frac{hc}{\lambda}, where h is Planck's constant (6.626 \times 10^{-34} \text{ J s}), c is the speed of light (3.00 \times 10^8 \text{ m/s}), and \lambda is the wavelength in meters. Convert the wavelength from nanometers to meters.

Determine the number of photons by dividing the total energy output by the energy of a single photon.

Ensure all units are consistent throughout the calculations to maintain accuracy.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Power and Energy

Power is defined as the rate at which energy is transferred or converted. In the context of the question, power is measured in watts (W), where 1 W equals 1 joule per second (J/s). Understanding this relationship is crucial for calculating the total energy output of the laser over a given time period, which is necessary to determine the number of photons emitted.

Photon Energy

The energy of a photon can be calculated using the equation E = hc/λ, where E is the energy, h is Planck's constant, c is the speed of light, and λ is the wavelength of the photon. In this case, the wavelength of the semiconductor laser is 780 nm. Knowing the energy of a single photon allows us to relate the total energy output of the laser to the number of photons emitted.

Time and Total Energy Calculation

To find the total energy output of the laser over the duration of the CD playback, we multiply the power of the laser by the total time in seconds. For a CD that plays for 69 minutes, this involves converting minutes to seconds and then using the power level of 0.10 mW to calculate the total energy. This total energy can then be divided by the energy per photon to find the total number of photons emitted.

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Certain elements emit light of a specific wavelength when they are burned or heated in a non-luminous flame. Historically, chemists used such emission wavelengths to determine whether specific elements were present in a sample. Some characteristic wavelengths for a few of the elements are given in the following table:

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