Why Do Electrons Closer to Nucleus Have Less Energy?

[DeathKnight]

Some one please make me understand why electrons closer to the nucleus have less energy than the ones which are farther from it. Is it because they have more potential energy?
Secondly, How do we know that protons exist as particles but not as a ball of positive charge.
Thanks in advance for any help...

 

[mrjeffy321]

The energy if an electron can be described by the following equation,
E = -b / n^2
Where E is energy,
b is a constant equal to (2*pi^2 * m_e^4)/h^2, where m is the mass of the electron, and h is Plank's Constant, so evaluated, b = 2.18E-18 J,
and n is the principle quantum number describig which electron shell the electron resides in.
So as you can see, as the electron goes into higher and higher shells (higher n values), the energy goes to smaller and smaller negative values for energy.

The energy an electron has around an atoms is it potential energy from the nucleus. The farther away from the nucleus, the more potential energy it has, up until it is completely removed from the atom, at which case it has zero potential energy.


We know the nucleus has a positive charge, which is the heaviest, most dense part of an atom. We also know that that amount that it is positive only comes in "packets" of a certain charge to cancel out the charge on an electron, so you can't have 3.4 + charges since they come in whole numbers in the form of a proton, just like you can't have 3.4 negative charges since you can only have whole numbers of electrons.
Then we can also predict how many protons a certain element should have (Hrogen 1, Sodium 11, ...), but if you "weight" the atom, the weight usually comes out to be more than the predicted weight, sometimes double or more. So we know that there must be something else in the nucleus that is contributing to the overall weight, but no the charge, thus neutrons and not just one blob of positive charge.

 

[ravenprp]

The energy of an electron in an atom is determined by its distance from the nucleus. As an electron gets closer to the nucleus, it experiences a stronger attraction to the positively charged protons in the nucleus. This attraction decreases the electron's potential energy, which is the energy an object has due to its position or configuration. Therefore, electrons closer to the nucleus have less potential energy than those farther away.

We know that protons exist as particles because of experiments and observations that have been conducted over many years. For example, the famous gold foil experiment conducted by Ernest Rutherford in 1911 showed that atoms have a small, dense, positively charged nucleus at their center. This led to the discovery of the proton as a subatomic particle with a positive charge. Additionally, advancements in technology, such as particle accelerators, have allowed us to directly observe and study protons as individual particles. So, while we cannot see protons with the naked eye, we have strong evidence to support their existence as particles rather than a "ball of positive charge."