# Electron Cloud

### quantum nucleus probability distribution

The term **electron** cloud is used to describe the area around an atomic nucleus where an electron will probably be. It is also described as the "fuzzy" **orbit** of an atomic electron.

An electron bound to the nucleus of an atom is often thought of as orbiting the nucleus in much the same manner that a **planet** orbits a **sun**, but this is not a valid visualization. An electron is not bound by gravity, but by the **Coulomb force**, whose direction depends on the sign of the particles' charge. (Remember, opposites attract, so the **negative** electron is attracted to the positive **proton** in the nucleus.) Although both the Coulomb force and the gravitational force depend inversely on the square of the **distance** between the objects of interest, and both are central forces, there are important differences. In the classical picture, an accelerating charged particle, like the electron (a circling body changes direction, so it is always accelerating) should radiate and lose **energy**, and therefore **spiral** in towards the nucleus of an atom... but it does not.

Since we are discussing a very small (microscopic) system, an electron must be described using quantum mechanical rules rather than the classical rules which govern planetary **motion**. According to **quantum mechanics**, an electron can be a wave or a particle, depending on what kind of measurement one makes. Because of its wave nature, one can never predict where in its orbit around the nucleus an electron will be found. One can only calculate whether there is a high probability that it will be located at certain points when a measurement is made.

The electron is therefore described in terms of its probability distribution or probability **density**. This probability distribution does not have definite cutoff points; its edges are somewhat fuzzy. Hence the term "electron cloud." This cloudy probability distribution takes on different shapes, depending on the state of the atom. At room **temperature**, most **atoms** exist in their lowest energy state or "ground" state. If energy is added-by shooting a **laser** at it, for example-the outer electrons can "jump" to a higher state (think larger orbit, if it helps). According to quantum mechanical rules, there are only certain specific states to which an electron can jump. These discrete states are labeled by *quantum numbers*. The letters designating the basic quantum numbers are *n*, *l*, and *m*, where *n* is the principal or energy **quantum number**, *l* relates to the orbital angular **momentum** of the electron, and *m* is a magnetic quantum number. The principal quantum number *n* can take integer values from 1 to **infinity**. For the same electron, *l* can be any integer from 0 to (*n* - 1), and *m* can have any integer value from -*l* to *l*. For example, if *n* = 3, we can have states with *l*= 2, 1, or 0. For the state with *n* = 3 and *l* = 2, we could have *m* = -2, -1, 0, 1, or 2.

Each set of *n, l, m* quantum numbers describes a different probability distribution for the electron. A larger *n* means the electron is most likely to be found farther from the nucleus. For *n* = 1, *l* and *m* must be 0, and the electron cloud is spherical about the nucleus. For *n* = 2, *l* = 0, there are two concentric spherical shells of probability about the nucleus. For *n* = 2, *l* = 1, the cloud is more barbell-shaped. We can even have a daisy shape when *l* = 3. The distributions can become quite complicated.

Experiment has verified these distributions for one-electron atoms, but the wave function computations can be very difficult for atoms with more than one electron in their outer shell. In fact, when the motion of more than one electron is taken into account, it can take days for the largest computer to output probability distributions for even a low-lying state, and simplifying approximations must often be made.

Overall, however, the quantum mechanical wave equation, as developed by Schrödinger in 1926, gives an excellent description of how the microscopic world is observed to behave, and we must admit that while quantum mechanics may not be precise, it is accurate.

## User Comments

almost 3 years ago

Conner Patton

Thank you! i am using this to help me in my research paper over the quantum mechanical model. Just wish i could have found the author name on the webpage to make it easier to site.

over 5 years ago

WELL i THiNk SCiENCE IS A LiL CONFUSiNq BUt MA SCiENCE tEACHERS rOCkkS. I NEEd tO dO A PROJECt ANd i NEEd A PiCtURE OF tHE ELECTRON CLOUD ANd i DONt kNOW HOW iT LOOkS :O. HELP?

over 2 years ago

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over 2 years ago

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over 2 years ago

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almost 3 years ago

Conner Patton

Thank you! i am using this to help me in my research paper over the quantum mechanical model. Just wish i could have found the author name on the webpage to make it easier to site.

about 3 years ago

Jessica Tucker

This helps me a lot with my school project, Thanks! <3

about 3 years ago

This is helpful. :DD Thankies. ^^

over 3 years ago

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over 5 years ago

i love learning about new things and i think its really fun knowing different stuff that u have never heard of

over 5 years ago

this is so cool

over 3 years ago

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over 5 years ago

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over 2 years ago

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5 months ago

lol lmao

5 months ago

maddie myers

this is stupid all this is is a lie

8 months ago

jessica

., it can help me a lot for my report .. tnx :)

about 1 year ago

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over 1 year ago

Hey I think you should put an MLA citation in this, or if not, at least put the author name and the date it was published, etc. for us to be able to cite it! THANKYOU

over 1 year ago

Hey I think you should put an MLA citation in this, or if not, at least put the author name and the date it was published, etc. for us to be able to cite it! THANKYOU

over 1 year ago

,,,thank a lot, now i understand what is the electron clouds are,,,,

over 1 year ago

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over 1 year ago

cierra brown

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almost 2 years ago

Eric

So is the shape of the electron cloud dependent on temperature (you said "at room temperature . . .

".

Please email me to discuss it; I probably won't check back on this page.

almost 2 years ago

rosemarry

i can understand nothing at all.

about 2 years ago

this was vary helful