In the hydrogen atom, what is the physical significance of the state for which n=∞and E=0 ?

Name: Problem 34, Chapter 7: Chemistry
Uploaded: 2019-08-15T15:18:59-08:00
Duration: 3 min 46 s
Channel: James Irizarry
Description: In the hydrogen atom, what is the physical significance of the state for which n=∞and E=0 ?

In the hydrogen atom, what is the physical significance of...

Key Concepts

Ionization Threshold

In quantum mechanics, the ionization threshold is the energy level at which an electron transitions from being bound to an atom to becoming free. For the hydrogen atom, as the principal quantum number approaches infinity, the binding energy approaches zero, marking the critical point where any additional energy will allow the electron to escape the atomic potential completely.

Bound versus Continuum States

Quantum systems like the hydrogen atom exhibit discrete (bound) energy levels for which the electron is confined and a continuum of energy levels for which the electron is free. The state with a principal quantum number of infinity and zero energy represents the boundary between these two regimes, where the electron is no longer bound and is at the threshold of entering the continuum of unbound or scattering states.

Scattering States

Scattering states refer to the quantum states of particles that are not confined by the potential and can move freely. In the context of the hydrogen atom, the state at zero energy signifies the point at which the electron has just enough energy to escape the attractive Coulomb potential, thereby transitioning from a bound state to a scattering state in the continuum.

Transcript

00:01 Humdrum was the physical significance of the state for which and equals infinity and e equals zero.

00:06 This problem for the two of chapter seven.

00:09 So when an is equal to infinity is gonna be equal to zero.

00:13 So let's let's look at our bormann.

00:17 We have and equals one and equals two and equals three.

00:29 And then n equals four and equals five and equal six eggs and uncle 77 and over here we have energy.

00:38 But remember ever the energy of the with the energy at this level at the lower levels.

00:47 This is going to be negative because when you have negative energy energy that shows that us bearable interactions, these would be the interactions between your electrons and and you're positively charged nucleus nucleus.

01:03 So i just put minus in parentheses.

01:06 So as you go higher and higher end values, you're moving further, your electrons moving further and further away from nucleus, so us nucleus.

01:15 And as you're goingto nichols, infinity e is going to eat.

01:19 E is going t equals zero teacup because after a certain point, you're not gonna be you're not really gonna feel the interaction between you're you're a negative charge lecture on you're positively charged nucleus.

01:32 So you're not going to see any kind of energy.

01:36 You're not really going to see any kind of energy in this energy in the system.

01:41 So you can kind of rewrite this graph as and e as looking something like this because us, because remember that that's an is just a function of the distance away from the new.

02:01 So remember that you go...

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