Questions about the energy level [ENDORSED]

[Karina Jiayu Xu 4E]

Can someone explain the relationship between energy level (n) and energy?
I think they’re inversely related but I’m not sure how it works conceptually..

[Samantha Pacheco 2K]

As n increases the energy of the electron increases as well. As n increases the e- moves farther away from the nucleus which means that the attraction between the nucleus and the e- will be weaker and the e- will be more unstable(as energy increases stability of e- decrease). Therefore the electron can be more easily ejected.

[EllerySchlingmann1E]

Hi,

Energy and energy level are related through the formula: E(n)=-hR/n^2, where E is the energy of the electron, n is the energy level, h is Planck's constant, and R is the Rydberg constant. You're right, in the equation energy and energy level are inversely proportional, but this is because we have to remember our point of reference.

Our point of reference is when n=>∞ and E=>0, making all other energies negative. One way to think about the relationship is to think that as the electron goes up in energy level (n increases), the electron's energy becomes smaller (gets less negative). The most energy an electron can have is when n=1, which is when the energy is also most negative, so any energy smaller than that is less negative. Though energy and energy level are inversely proportional in the equation, it's due to the nature of our reference point. Hope that can clear at least a bit of this concept up!

[SophiaKohlhoff4B]

To think this through the relation of energy and wavelength formulaically, consider the formula: wavelength = hc/E. Because h and c are both constants, the numerator will always equal the product of Planck's constant and the speed of light. Wavelength will therefore decrease as energy, E, increases. To then consider the impact of energy level (n) on wavelength: An increase in n will increase the energy of the electron, decreasing the wavelength.