(a) Ozone formation in the upper atmosphere starts when...

(a) Ozone formation in the upper atmosphere starts when oxygen molecules absorb UV radiation with wavelengths less than or equal to $242 \mathrm{nm}$. Find the frequency and energy of the least energetic of these photons. (b) Ozone absorbs radiation with wavelengths in the range $2200-2900$ A thus protecting organisms from this radiation. Find the frequency and energy of the most energetic of these photons.

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Key Concepts

Unit Conversion

Accurate physics calculations often require converting between different units, such as converting wavelengths expressed in nanometers or angstroms into meters. Unit conversion ensures that all parts of an equation are consistent, thereby yielding correct results in energy and frequency computations.

Planck?Einstein Relation

This fundamental principle in quantum mechanics states that the energy of a photon is directly proportional to its frequency, given by the equation E = h? (or equivalently E = hc/?). It serves as the basis for calculating photon energies and illustrates the quantization of electromagnetic radiation.

Wavelength?Frequency Relationship

The relationship between wavelength (?) and frequency (?) is defined by the equation c = ??, where c is the speed of light in a vacuum. This concept is essential for converting the wavelength information of electromagnetic radiation to its frequency, which is then used in energy calculations.

Electromagnetic Spectrum

Understanding the range of wavelengths (or frequencies) within the electromagnetic spectrum is crucial when dealing with various types of radiation such as ultraviolet, visible light, and infrared. This knowledge helps in identifying which part of the spectrum is involved in phenomena like photodissociation or absorption processes.

Transcript

00:01 In this problem, we will be solving for the frequency and the energy of electromagnetic radiation of two different wavelengths.

00:11 Part a starts by asking us to find the frequency and the energy of the least energetic of the named photons.

00:19 The photons in question are 242 nanometers or less in wavelength.

00:25 So finding the least energetic of these photons, we know that we would use the high.

00:31 Highest wavelength, which would be 242 nanometers.

00:35 We know this by the relationship between the energy to the wavelength.

00:40 The wavelength in this equation is on the denominator, showing that as this number goes up, the energy would go down.

00:50 Vice versa, as this energy goes down, this energy would go, as this number goes down, this energy would go up.

00:59 So we know that we're starting with 242 nanometers to solve for our frequency and then our energy.

01:05 First thing we need to do is to convert our nanometers into normal meters.

01:10 We can do this through a convenient little conversion chart that i drew at the top.

01:15 We know that nanometers is 10 to the negative niths to convert it to meters.

01:20 So using this conversion, we can go ahead and write our wavelength like this.

01:30 After we've done this, we can plug it into our first equation, which relates our frequency to our wavelengths...

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