How much energy is contained in 1 mol of each? a. X-ray photons with a wavelength of 0.135 nm b.

How much energy is contained in 1 mol of each? a. X-ray...

Key Concepts

Energy Unit Conversion

Energy unit conversion involves translating calculated energy values into standard units such as joules. When dealing with macroscopic quantities like a mole of photons, it is critical to manage unit conversions carefully to ensure that the final energy value is expressed in the desired and correct units.

Avogadro's Number

Avogadro's number is a constant (approximately 6.022 x 10^23) that represents the number of particles in one mole of a substance. It is used to convert the energy of a single photon into the energy contained in one mole of photons by multiplying the energy per photon by this large number.

Photon Energy Quantization

Photon energy quantization refers to the concept that light consists of individual energy packets called photons, with each photon having an energy that is directly proportional to its frequency and inversely proportional to its wavelength. This idea is fundamental to quantum mechanics and explains how light interacts with matter.

Planck's Equation

Planck's equation, E = hc/?, is the formula used to calculate the energy of a single photon, where E is the photon energy, h is Planck's constant, c is the speed of light, and ? is the wavelength of the photon. This relationship is essential in understanding the energy properties of electromagnetic radiation.

Transcript

00:01 This question covers relating the energy contained in one mole of photons of light to the wavelength of that photon.

00:11 And the two examples that we're given are an x -ray and a gamma ray.

00:17 And we're going to go ahead and start off with our x -ray.

00:20 And the x -ray photon wavelength, which is given by lambda, is equal to 0 .135 nanometers.

00:30 Now i have gone ahead and written this equation up at the top, which relates our energy, overhand left, to an expression of planx constant, the speed of light, and that number, which we have just given lambda.

00:44 So now that we have lambda defined, we can go ahead and use these constants to determine the energy.

00:52 And the way that we would do that, as we would say energy, is equal to, let's go ahead and do this in a different color.

01:01 About blue.

01:03 Energy is equal to planks constant, which is 6 .626 times 10 to the minus 34.

01:16 I'm not going to write down units, but we're going to be using all si units for the purposes of this exercise.

01:21 So 6 .626 times 10 to the minus 34 times we have 2 .99 times 10 to the 8 meters per second for the speed of light over 0 .135 or nanometers, so to get back to meters, we have to multiply by times 10 to the minus 9.

01:44 And this would give us the energy per particle.

01:47 To get the energy per mole, we need to multiply by 6 .02 times 10 to the 23rd photons per mole.

02:02 And we're going to go ahead and plug that into our calculator and see what it is when we get back.

02:10 And okay, when we go ahead and do that, we're going to see that...

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