## why is Bohr Frequency equation negative

H-Atom ($E_{n}=-\frac{hR}{n^{2}}$)

Ya Gao
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### why is Bohr Frequency equation negative

Can somebody please tell me why there is a negative sign in the equation ∆E=-hR/n2. I didn't quite get that in the class and why n approaches infinity the energy of the electron will be 0? Doesn't it have to receive a ton of energy to be excited to the outer levels?? I'm so confused.

Mika Sonnleitner 1A
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### Re: why is Bohr Frequency equation negative

The equation E=-hR/n^2 represents the change of energy level that an electron goes through when there is a light source with enough energy to move the electron. An important thing to note: as the energy level approaches infinity, E approaches 0 (plug in infinity for the "n" in the equation). So, the reference point used for all elements is E=0, because when the electron is completely removed, it is too far to interact with the nucleus. Since E approaches 0 as we increase energy levels, you should think of 0 as the highest point, and all energy levels below it as negative.

For example, when an electron moves from the n=4 energy level to the n=2 energy level, it emits energy, and also moves down energy levels, meaning that energy is negative because it moves below 0. Basically, the negative sign means that an electron that is bound to the nucleus has a lower energy than an electron that is free/far away from the nucleus.

However, when plugging in the calculated energy into another equation (to solve for wavelength or frequency, for example), you would plug in the positive energy value, even though energy from your calculations is negative. This is because the electron emits energy as electromagnetic radiation, representing a decrease in energy. But, for purposes of further calculations you must use a positive energy value, to avoid getting a negative wavelength or frequency as your answer.

Angel Gomez 1K
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### Re: why is Bohr Frequency equation negative

Different elements have different characteristics, so the energy at the ground state of an electron (e-) for Hydrogen (H) is going to be different than the energy for the ground state of an e- of Helium (He), for example. The energy for a hydrogen e- at the ground state is 2.178 x 10^-20 Joules (J), and that number isn't the same for any other element. For that reason, energy (E) is measured at 0 when the e- is ionized, or free from the atom. The value of the ground state is the most negative because that amount of negative energy is what is required in the positive form to remove the e-. If you notice, the next level is also negative, but still a value closer to zero. As the levels increase, there is less of a distance between how much energy is needed to reach the next level. Therefore, the higher the level, the less energy that is needed to pull the e- away and have it unbound. It's a bit confusing, but if you also look at the equation, you can see that the larger the value of n, the closer the value of ΔE is to 0.
Here's a link that might be of use:
http://astro.unl.edu/naap/hydrogen/levels.html

Kellina Tran 2I
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### Re: why is Bohr Frequency equation negative

To sum it up, I believe that the negative sign represents the idea that the energy being used to remove the electron (a positive value) must match and thus cancel out the negative value of the required energy to move the electron. As the electron moves from a higher to lower energy level, the energy of the electron becomes closer to 0 as it is emitting energy. Please correct me if I am wrong.

Tasnia Haider 1E
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### Re: why is Bohr Frequency equation negative

As the electron returns to a ground state, it's point of reference was at the highest energy level who's energy was zero. Since the electron is returning to a lower energy level, it is emitting energy and would have to be a negative number because of the reference point's energy which is zero.