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Ch.6 - Electronic Structure of Atoms
Brown - Chemistry: The Central Science 14th Edition
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Tutti i libri di testoBrown 14th EditionCh.6 - Electronic Structure of AtomsProblema 32
Capitolo 6, Problema 32

A stellar object is emitting radiation at 3.0 mm. (a) What type of electromagnetic spectrum is this radiation (b) If a detector is capturing 3.0 3 108 photons per second at this wavelength, what is the total energy of the photons detected in 1 day?

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Step 1: Identify the type of electromagnetic radiation. The wavelength of the radiation is given as 3.0 mm. This falls within the range of the microwave region of the electromagnetic spectrum. Therefore, the radiation is a microwave radiation.
Step 2: Calculate the energy of a single photon. The energy of a photon can be calculated using the formula E = h*c/λ, where E is the energy, h is Planck's constant (6.626 x 10^-34 J*s), c is the speed of light (3.0 x 10^8 m/s), and λ is the wavelength. Remember to convert the wavelength from mm to m before using it in the formula.
Step 3: Calculate the energy of all photons detected per second. Multiply the energy of a single photon by the number of photons detected per second (3.0 x 10^8 photons/second).
Step 4: Calculate the total energy of photons detected in 1 day. There are 86400 seconds in a day. Multiply the energy of all photons detected per second by the number of seconds in a day to get the total energy of photons detected in 1 day.
Step 5: The result from step 4 is the total energy of the photons detected in 1 day. Remember to express your answer in the correct units of energy (Joules).

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Electromagnetic Spectrum

The electromagnetic spectrum encompasses all types of electromagnetic radiation, which vary in wavelength and frequency. Radiation at 3.0 mm falls within the microwave region of the spectrum, which is used in various applications, including communication and cooking. Understanding the position of radiation within the spectrum helps in identifying its properties and potential uses.
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Electromagnetic Spectrum

Photon Energy

Photons are particles of light, and their energy is directly related to their frequency, as described by the equation E = hν, where E is energy, h is Planck's constant, and ν is frequency. For radiation at 3.0 mm, calculating the energy of individual photons requires converting the wavelength to frequency using the speed of light. This concept is crucial for determining the total energy of multiple photons.
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Photon Energy Formulas

Energy Calculation Over Time

To find the total energy of photons detected over a specific time period, one must multiply the energy of a single photon by the number of photons detected and the duration of detection. In this case, if 3.0 x 10^8 photons are captured per second, the total energy over one day (86,400 seconds) can be calculated by integrating these values. This concept is essential for understanding how energy accumulates from continuous photon detection.
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The Gibbs Free Energy Formula Example
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