According to the quantum-mechanical model for the hydrogen atom, which electron transition produces light with the longer wavelength: 3p → 2s or 4p → 3p?

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hey everyone in this example, we need to determine which of the following transitions. Produced a shorter wavelength. Based on the quantum model for the hydrogen atom. We should recall that when it comes to frequency of a wave length which is represented by this symbol. When we have a higher frequency. That will therefore correspond to higher energy, therefore corresponding to a short wavelength. And that is due to the fact that our wave is going to form much faster because the frequency is so high and the energy is so high. And so what we can say is that the larger the transition between energy levels we would say therefore the higher the energy emitted. So we want to go ahead and analyze our answer choices for the largest transition which will therefore correspond to a large emission of energy and therefore a short wavelength. So looking at choice a. We have the eight s. Orbital and we go up to the seven p orbital. However, we end up at a lower energy level being the seventh energy level. So we can go ahead and rule out choice A. Because this isn't an appropriate transition. Moving onto choice B. We go from the five P sublevel or yeah sub level to the to p sub levels. So we go to a lower energy sub level and our transition is only down to three units. So let's go ahead and compare this to choice see where we start from the six S. Sub level and go down to the three S sub level. So this is also three units down and energy. And lastly we have Choice D. Where we started the eight S. Sub level and go all the way down to the one S. Sub level. And so this is eight units down in a transition. This would be a pretty long transition, meaning we must have had a pretty high frequency for our wavelength to go down to such a dramatic transition in energy energy levels. So we can go ahead and rule out choices B and C. As well because our largest transition occurs and the transition described in choice D. And because this is the largest transition, we would say therefore we have a high frequency, a high energy and short wavelength. So the only correct choice to complete this example would be choice D. Where we go from the 80 S. Sub level down to the one S. Sub level to honor our quantum model for our hydrogen atom. So I hope that everything I explained was clear. If you have any questions, please leave them down below and I will see everyone in the next practice video.

According to the quantum-mechanical model for the hydrogen atom, which electron transition produces light with the longer wavelength: 3p → 2s or 4p → 3p?

Verified Solution

Key Concepts

Electron Transitions

Wavelength and Energy Relationship

Quantum Numbers and Energy Levels