The rays of the Sun that cause tanning and burning are in...

The rays of the Sun that cause tanning and burning are in the ultraviolet portion of the electromagnetic spectrum. These rays are categorized by wavelength. So-called UV-A radiation has wavelengths in the range of $320-380 \mathrm{nm},$ whereas UV-B radiation has wavelengths in the range of $290-320 \mathrm{nm} .$ (a) Calculate the frequency of light that has a wavelength of 320 $\mathrm{nm}$ . (b) Calculate the energy of a mole of 320 -nm photons. (c) Which are more energetic, photons of UV-A radiation or photons of UV-B radiation? (d) The UV-B radiation from the Sun is considered a greater cause of sunburn in humans than is UV-A radiation. Is this observation consistent with your answer to part (c)?

Key Concepts

Frequency-Wavelength Relationship

The frequency and wavelength of electromagnetic waves are inversely related through the speed of light. This relationship is expressed by the formula c = ??, where c is the speed of light, ? is the wavelength, and ? is the frequency. It is a fundamental concept that enables the calculation of one parameter when the other is known, which is essential in analyzing radiation properties.

Radiation Wavelength and Energy Comparison

The energy carried by electromagnetic radiation is inversely related to its wavelength; shorter wavelengths correspond to higher frequencies and thus higher energies per photon. This principle allows us to compare different types of radiation, such as various bands in the ultraviolet spectrum, in terms of their potential to impart energy and cause effects like tanning or burning.

Avogadro's Number and Molar Energy

Avogadro's number defines the number of particles in one mole of any substance, linking microscopic photon energies to macroscopic energy quantities. By multiplying the energy of a single photon by Avogadro's number, one can calculate the total energy contained in a mole of photons, bridging quantum-scale phenomena and practical, measurable energy values.

Electromagnetic Spectrum

The electromagnetic spectrum encompasses all types of electromagnetic radiation arranged according to their wavelength or frequency. This concept is central to understanding how different forms of radiation—from radio waves to gamma rays—interact with matter. In particular, ultraviolet radiation is a portion of this spectrum characterized by wavelengths shorter than visible light, which influences both its effects and its energy characteristics.

Photon Energy

Photon energy is the amount of energy carried by individual quanta of electromagnetic radiation. It is directly proportional to the frequency of the light and is determined by the equation E = h?, where h refers to Planck's constant. This concept is critical in understanding how electromagnetic energy interacts with matter at the atomic and molecular levels.

Planck's Constant

Planck's constant is a fundamental physical constant that relates the energy of a photon to its frequency. It is a cornerstone in quantum mechanics, providing the basis for calculations involving photon energies and laying the groundwork for understanding phenomena such as quantization and the photoelectric effect.

Transcript

00:01 All right, so this question is about the uv radiation.

00:03 There are two types of them, the uva and the uvb.

00:06 And the uva has wavelength in the region of 320 nanometers to 380 nanometers, and uvb has wavelength in 290 to 320 nanometer.

00:17 So we are told to calculate the frequency of uv radiation with 320 nanometer.

00:23 So frequency, we know is c, the variable lambda, where c is the speed of light.

00:27 So c here is 3 times 10s per second and lambda is 320 nanometer.

00:35 So 1 nanometer is 10x per minus 9 meter.

00:37 So that's times 10x per minute.

00:40 So if you punch the calculator, this will give you 9 .375 10 10 10 .14 per seconds.

00:47 Then we are told to calculate the energy of this 320 nanometer wavelength.

00:52 So basically what we just need to do is to say that the relationship between energy and wavelength is e is equal to hc of a lambda.

01:01 We are h is a plant constant and that is 6 .6 to 6 .6 times times per minus 34 joules seconds and the speed of light is 3 times times per 8 and wavelength is 320 times per minus 9 meters.

01:14 So punching the calculator, they should give us 6 .2 .1 times times per minus 90 joules.

01:20 Then we need to calculate the energy of one mole of photon.

01:25 So we know one more or photon contains 6...

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