The most prominent line in the spectrum of magnesium is 285.2 nm . Other lines are found at 383.

The most prominent line in the spectrum of magnesium is...

The most prominent line in the spectrum of magnesium is $285.2 \mathrm{nm} .$ Other lines are found at 383.8 and $518.4 \mathrm{nm} .$ In what region of the electromagnetic spectrum are these lines found? Which is the most energetic line? What is the energy of 1 mol of photons with the wavelength of the most energetic line?

Key Concepts

Electromagnetic Spectrum

This concept refers to the complete range of wavelengths or frequencies of electromagnetic radiation. It includes various regions such as radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays. Understanding the electromagnetic spectrum is crucial for identifying which region a specific wavelength belongs to and for analyzing the properties of light, including energy levels and transitions in atoms.

Photon Energy Calculation

Photon energy is determined by the relationship E = hc/?, where E is the energy of a photon, h is Planck's constant, c is the speed of light, and ? is the wavelength. This equation shows that energy and wavelength are inversely related, meaning that shorter wavelengths correspond to higher energies. This concept is fundamental in quantum mechanics and spectroscopy for understanding how photons interact with matter.

Mole Concept in Photonic Energy

The mole concept allows the calculation of the total energy contained in a large number of photons, specifically Avogadro's number of photons (approximately 6.022 x 10^23). By using the energy of a single photon and multiplying by Avogadro's number, one can determine the energy per mole of photons, which is important in chemical thermodynamics and photochemistry for scaling microscopic properties to macroscopic quantities.

Transcript

00:01 All right, to start off, we're going to be looking out where the wavelengths are.

00:06 So i put up a little visible spectrum with the wavelengths on there, if you can see.

00:13 And so 285 .2, sorry, nanometers is going to be off the visible spectrum in the ultraviolet spectrum, right? 383 .8 is going to be, this graph has it kind of in.

00:31 They're violet, but it's still very dark, if you can tell.

00:35 So i'm going to classify that under ultraviolet again.

00:39 And then the 518 .4, that one is actually going to be in the green, in our actual visible spectrum.

00:50 And so next we're going to be figuring out which of these three numbers is going to be our most energetic version.

00:58 So we know that the energy follows an inverse pattern with our wavelengths.

01:06 So the lower the number, lower the wavelength, higher the energy.

01:13 So in this case, that's going to be 285 .2 nanometers.

01:19 So our next goal for this problem is we want to find out what our frequency is so that way we can put that into our next equation.

01:30 To figure out how much energy it has.

01:35 So we're going to use this equation, which is going to be equal to the speed of light, which means frequency is equal to the speed of light, which is 2 .998 times 10 to the 8th meters per second over our wavelength that we figured was 285 nanometers.

01:54 You want to keep it in the meters, however, because you want to be able to, negate them for when you do your division.

02:05 So times 10 to negative 9 because there's a billion nanometers for every meter...

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