Calculate the wavelength and frequency of light emitted when an electron changes from n=4 to n=3

Calculate the wavelength and frequency of light emitted when...

Key Concepts

Electromagnetic Spectrum

The electromagnetic spectrum encompasses all wavelengths of electromagnetic radiation, from radio waves to gamma rays. Understanding this spectrum allows one to classify the radiation emitted from atomic transitions, such as identifying whether the radiation falls within the visible, infrared, ultraviolet, or another region based on its calculated wavelength and frequency.

Photon Energy Relationships

Photon energy is directly related to its frequency and inversely related to its wavelength through the equations E = hf and E = hc/?, where h is Planck's constant and c is the speed of light. These relationships are crucial for converting between measured wavelengths, frequencies, and energy changes during electron transitions.

Bohr Model

The Bohr model explains that electrons in atoms exist in discrete energy levels and that transitions between these levels result in emission or absorption of radiation. It is fundamental in understanding how quantized energy differences lead to the generation of light at specific wavelengths.

Rydberg Formula

The Rydberg formula is used to calculate the wavelengths of light emitted or absorbed by hydrogen atoms due to electron transitions between energy levels. It connects the inverse of the wavelength with the difference in the reciprocals of the squares of the principal quantum numbers.

Transcript

00:01 All right, so for this question, they're asking for our wavelength and frequency and where on the spectrum it comes up for n equals 4 to n equals 3.

00:09 Right.

00:10 So our first step is to figure out how much energy that is.

00:14 We do that by using the delta energy equation where you subtract the final energy by the initial energy, and you find that by multiplying the, i believe that's the rhc, which stands for three.

00:32 Different constants and those constants are the rydberg constant the planks constant and the speed of light and then you can multiply that by one over the quantum state squared for each one right so this one will be corresponding to the initial or the final energy and this one will be corresponding to the initial or the final energy and this one will be corresponding to the initial energy.

01:11 So then we can just plug those numbers in.

01:15 So negative rhc times one ninth because it's the third quantum state for the final and the fourth quantum state for this initial.

01:29 We multiply that out and you get 0 .0486.

01:33 You still have to multiply it by your constants or if you multiply those you find that that's a 1 ,312 kilojoules per mole and that gives you minus 63 .78 kilojoules per mole.

01:51 It's negative because we're going from a higher state to a lower state, therefore releasing energy in emission, right? but then you might be wondering, we need our joules per photon because you can't really calculate wavelength with this high of energy.

02:09 So we multiply that by a thousand because there's a thousand...

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