# Energy levels in an atom

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When I was taught energy levels in a hydrogen atom – I was given the formula ;Energy = -13.6/n^2.

(1)What purpose does that minus sign signify?

(2)If energy in the first Bohr orbit is -13.6 and in the second one is -3.4 is:

(a) The energy in the second orbit greater as
-3.4 > -13.6 or
(b) The energy in the first orbit is greater as
|-13. 6| > |-3.4|?
Is there a better way to look at the energy values (as the minus sign is confusing)?

In: 12 So, any time you express the energy of a state, it’s in reference to something else. To some extent, that reference energy is totally arbitrary; what matters is if the energy of something you’re describing is higher or lower than that reference.

In the case of electrons associated with an atom, the most common reference energy is the state where the electron is at rest and infinitely far away from a nucleus. That state is considered 0 eV.

Now, imagine moving the electron towards a positively charged nucleus. Opposite charges attract, and the energy of the electron goes down the closer you get to the nucleus (until you get really, REALLY close, but that’s >ELI5). Started at 0 and decreasing, energy level of an electron becomes more and more negative the closer you get.

The 1s orbital is closer to the nucleus than the 2s one, so the 2s has a higher energy than 1s. The energy of an electron is more a measure of the potential energy of the attraction between positive nucleus and negative electron. For attractive forces, the further away something, the more PE it will have (like gravity). Therefore, outer orbits have more energy than lower orbits.

But what is the maximum energy? If PE increases with distance, then an electron infinitely far from the nucleus would have maximum energy.

However, we also know that attractive forces diminish over distance. An infinitely far electron does not exert much attraction on the nucleus (and vice versa). So we say an infinitely far electron has zero potential energy.

Using this *zero energy reference point*, we can consider an electron approaching the nucleus. Recall that the closer the electron is, the less PE it will have. If the maximum energy is zero, and it only decreases, then the energy of an electron can only be negative. 1. The purpose of the minus sign is to show it takes energy to remove an electron as it is attracted to the positive nucleus. Imagine two pieces of velcro stuck together, and if you want to separate them, you have to add energy. Same thing with electrons in atoms.

2. This links to the first part. The further away the electron is from the nucleus, the less energy it takes to remove. Now imagine velcro is less sticky. Its easier to separate. 0 energy would be a free electron. If it had positive energy, then its a free electron moving around with kinetic energy. If it has negative energy, we know it’s tied to an atom and we can figure out exactly how much energy it takes to free the electron.

The 0 point for energy is completely arbitrary, but we just chose that 0 point because it makes the math easier.