Why do electrons in lower atomic orbits have smaller wavelengths?

In summary, according to the Virial theorem, electrons in lower energy levels have smaller wavelengths and higher frequencies compared to electrons in higher energy levels. This may seem counterintuitive since lower energy levels are typically associated with lower energies, but this is because the potential energy in lower energy levels is much more negative to balance out the higher kinetic energy.
  • #1
daisey
131
3
I was previously under the impression that an atomic electron in its lowest orbit has a larger wavelength than an electron in a higher atomic orbit. I read earlier today that lower orbiting electrons actually have smaller wavelengths. :confused:

This seems backwards since electrons naturally try to settle into lower orbits, which have lower energies (I thought). And I normally equate energy with wavelength.
 
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  • #2
daisey said:
I was previously under the impression that an atomic electron in its lowest orbit has a larger wavelength than an electron in a higher atomic orbit. I read earlier today that lower orbiting electrons actually have smaller wavelengths. :confused:

This seems backwards since electrons naturally try to settle into lower orbits, which have lower energies (I thought). And I normally equate energy with wavelength.

Energy is proportional to frequency, which means it's *inversely* proportional to wavelength.
 
  • #3
PeterDonis said:
Energy is proportional to frequency, which means it's *inversely* proportional to wavelength.
So electrons in lower orbits have...

* Relatively less energy
- Higher Kinetic Energy
- Lower Potential Energy
* Smaller Wavelength
* Higher Frequency
 
  • #4
Wavelength isn't something that is well defined for an electron in an atom, for the same reason that momentum [tex]p = \hbar/\lambda[/tex] can't be well defined; the potential keeps the electron from settling into a momentum eigenstate.

You can do things like compute the expectation value of kinetic energy [tex]1/2m \langle p^2 \rangle[/tex] which will be non-zero. And it will be true that electrons in lower energy levels will have more kinetic energy, but they will also have a much more negative potential energy. In fact, the Virial theorem applies, so [tex]\langle V \langle = -2\langle T \rangle[/tex], so an electron in a state with large kinetic energy will have a much larger potential energy than an electron in a state with low kinetic energy.
 

1. What is the energy of atomic electrons?

The energy of atomic electrons refers to the amount of energy that an electron possesses while orbiting around the nucleus of an atom. This energy is quantized, meaning it can only exist in certain discrete levels or states.

2. How is the energy of atomic electrons measured?

The energy of atomic electrons is measured in units of electron volts (eV) or joules (J). This can be done using spectroscopy techniques, such as photoelectron spectroscopy, which measures the energy of electrons that are ejected from the atom.

3. What factors affect the energy of atomic electrons?

The energy of atomic electrons is affected by the charge of the nucleus, the distance between the electron and the nucleus, and the quantum state of the electron. The energy also varies depending on the type of atom and the number of electrons present.

4. Why is the energy of atomic electrons important?

The energy of atomic electrons is important because it determines the chemical and physical properties of an element. It also plays a crucial role in chemical reactions and the formation of chemical bonds between atoms.

5. How does the energy of atomic electrons change in different elements?

The energy of atomic electrons varies in different elements due to the different number of protons and electrons in each atom. The number of electrons and their arrangement in the atom's energy levels determine the specific energy values for each element.

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