Undergrad Atomic Structure: Why Does Energy Decrease with Orbit Number?

[Aurelius120]

TL;DR

Why does transition energy decrease with increase in orbit number?

I have read that an electron requires certain minimum energy of threshold frequency to move an orbit

However the energy needed decreases with increase in shell number

The transition energy is reduced with each orbit

For example
The energy to shift an electron from 1st to 2nd orbit is much greater than that required to shift it from 2nd to 3rd (which is greater than from 3rd to 4th and so on)

This is what I don't understand
(Why is it greater)
No one seems to give the right answer

Please explain

 

[dlgoff]

Aurelius120
I have this paperback that will answer your questions:

Here's the search I just used to find it:
https://www.amazon.com/dp/0486601153/?tag=pfamazon01-20
Buy used now for $9.88-$14.95

 

[jtbell]

Look up the energy-level formula for hydrogen, which is the simplest atom. Calculate the energy levels for n = 1, 2, 3, 4. Maybe a few more values of n. Draw an energy-level diagram to scale, using these numbers. You should be able to see the pattern very clearly.

The book shown above almost certainly has a diagram like this. You can also find many similar diagrams (and the formula) with a Google search for "hydrogen energy levels."

If you really meant to ask, "why is the energy-level formula what it is?" then the answer is "solve the time-independent Schrödinger equation (specifically the radial portion) for the hydrogen atom."

 

[Aurelius120]

Thanks a billion

 

[OdiGeo]

TL;DR Summary: Why does transition energy decrease with increase in orbit number?

I have read that an electron requires certain minimum energy of threshold frequency to move an orbit

However the energy needed decreases with increase in shell number

The transition energy is reduced with each orbit

For example
The energy to shift an electron from 1st to 2nd orbit is much greater than that required to shift it from 2nd to 3rd (which is greater than from 3rd to 4th and so on)

This is what I don't understand
(Why is it greater)
No one seems to give the right answer

Please explain

The more spread out the orbit is the more leverage or influence outside forces have on said orbit...therefore less energy is required to move from one orbit to the next larger one than was required for the prior jump.

 

[phinds]

The more spread out the orbit is the more leverage or influence outside forces have on said orbit...therefore less energy is required to move from one orbit to the next larger one than was required for the prior jump.

That clearly makes no sense since the ratio of bonding strength of orbitals would be the same if the atom were the only atom in the universe.