Rydberg Equation and Negative Signs
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Rydberg Equation and Negative Signs
Hi, I had a quick question about how we should be leaving our answers when solving questions using the Rydberg equation/empirical equation. When using the Rydberg equation, we get a positive value, obviously because the answer is in Hz. Then we can convert to E which leaves us with a positive value. If an electron is falling from a higher energy level down to a lower energy level, releasing energy, should we be adding a negative sign in front? The empirical equation does leave the answer negative, so I'm not sure whether the positive or negative answer would be correct. Does it depend on the wording of the question like if it specifically asks for "change in energy" vs "how much energy was released?" I'm just worried exams might give us both answers as choices, I wouldn't know which one to go for.

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Re: Rydberg Equation and Negative Signs
I think if energy is being released you need to make the value positive because it is releasing it and not consuming energy which is implied with the negative. I remember in a step up session my ua said the value is always positive because the energy is being released. Hope this was helpful!

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Re: Rydberg Equation and Negative Signs
If an electron jumps from a high state of energy to a low energy state, the change in energy is negative because this process release energy. However, when we use the energy later to calculate either the frequency or the wavelength, we usually do not include the negative sign, or you can understand as we usually use the absolute value. This is because wavelength and frequency are always reported as positive quantities.
I think if the question asks about "change in energy", and you get a negative answer, it would be better if you just add a sentence like "that means nJ of energy is released".
I think if the question asks about "change in energy", and you get a negative answer, it would be better if you just add a sentence like "that means nJ of energy is released".

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Re: Rydberg Equation and Negative Signs
Hi! I wanted to add something that really helped me understand the right sign to use. For the Rydberg equation, we get a negative value because we are calculating the decrease in energy as the electron moves from a higher shell to a lower shell. However, when we use that value to calculate the frequency of light emitted, we would use a positive value because we are referring to the photon that released the same amount of energy while the electron moved. This explains Lavelle's example from the lecture. He essentially "got rid" of the negative sign from the Rydberg equation to use the E=hv equation (which referred to the photon, not the electron) in order to find the frequency of the light.

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Re: Rydberg Equation and Negative Signs
Hi! I agree with all the other answers here  in general, there is never going to be a loss of energy in the system because it is conserved and just transformed into different types of energy or transmitted to another object. I would say only if the question has wording similar to "total change in energy of the electron" and the electron is losing energy to use a negative sign. If the question asks how much energy is released or absorbed, make the answer positive.

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Re: Rydberg Equation and Negative Signs
Usually, the question will ask for something related to the magnitude of energy that was released. However, when you use the Rydberg Constant, you will usually be solving for the energy released by one single electron, so relatively, the energy will be negative. Hope this helps!

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Re: Rydberg Equation and Negative Signs
Tl;dr If the question asks about the energy of the electron it will be negative as it loses energy. If the question is asking how much energy is released or is in the photon released that is positive.

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Re: Rydberg Equation and Negative Signs
Catie Donohue 3I wrote:Hi! I agree with all the other answers here  in general, there is never going to be a loss of energy in the system because it is conserved and just transformed into different types of energy or transmitted to another object. I would say only if the question has wording similar to "total change in energy of the electron" and the electron is losing energy to use a negative sign. If the question asks how much energy is released or absorbed, make the answer positive.
What if you’re using the Rydberg equation but solving for some other component rather than the energy? If they give you the energy and you plug it into the equation, whether it is being emitted or absorbed, do u change the sign when plugging it into the problem? You say to maybe make the answer positive or negative if you’re solving for energy, but what if it is plugged in? Thank you!

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Re: Rydberg Equation and Negative Signs
Isabelle Hales 3L wrote:Hi! I wanted to add something that really helped me understand the right sign to use. For the Rydberg equation, we get a negative value because we are calculating the decrease in energy as the electron moves from a higher shell to a lower shell. However, when we use that value to calculate the frequency of light emitted, we would use a positive value because we are referring to the photon that released the same amount of energy while the electron moved. This explains Lavelle's example from the lecture. He essentially "got rid" of the negative sign from the Rydberg equation to use the E=hv equation (which referred to the photon, not the electron) in order to find the frequency of the light.
This makes sense, thank you! However, what if we use that energy value you used in your example to calculate the wavelength? Does it still stay positive?

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Re: Rydberg Equation and Negative Signs
If you're plugging in the energy to solve for other components then you should use the same sign that is given by the problem. The number n and frequency v is always positive in the answer.

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Re: Rydberg Equation and Negative Signs
When you're asked to calculate the energy that will be required or emitted, you should most likely leave the sign either negative or positive because it'd indicate whether energy was being released or absorbed. When you use that energy value in another equation, the negative sign is no longer necessary (it'll be positive) because that relationship of release/absorption is irrelevant to the calculation of wavelength/frequency/etc.

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Re: Rydberg Equation and Negative Signs
Yes, it still stay positive and wavelength is always positive. Think about the problem in this way: electron loses energy while dropping from a higher number of n to a lower one, therefore the energy is negative for electrons; the light that got emitted gains energy from the electron, therefore the energy is positive for the light thus its frequency and wavelength are both positive as well.
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