The snapshot of electrons "orbiting" the nucleus like planets around the sun continues to be an enduring one, not just in renowned images of the atom but likewise in the minds of countless of us who know better. The proposal, first made in 1913, that the centrifugal force of the revolving electron just specifically balances the attractive force of the nucleus (in analogy with the centrifugal force of the moon in its orbit precisely counteracting the traction of the Earth"s gravity) is a quite picture, however is simply untenable.

You are watching: The motion of electrons can be predicted precisely. Figure $$\PageIndex1$$: Most popular science pictures of the atom present electrons moving roughly a nucleus choose planets around the sun. These pictures are quite merely wrong. They come from an old idea around the structure of the atom and also have lasted, partially from habit, and also partly because the contemporary view of the plan of electrons in the atom is too daunting to draw basic pictures of.

One beginning for this hypothesis that argues this view is plausible is the similarity of the gravity and Coulombic interactions. The expression because that the pressure of gravity in between two masses (Newton"s law of gravity) is

\

with

$$m_1$$ and also $$m_2$$ representing the mass of object 1 and also 2, respectively and also $$r$$ representing the distance between the objects centers

The expression for the Coulomb force between two charged types is

\

with

$$q_1$$ and also $$q_2$$ representing the charge of thing 1 and also 2, respectively and $$r$$ representing the distance between the objects centers

However, one electron, uneven a planet or a satellite, is electrically charged, and also it has actually been known because the mid-19th century that an electric charge the undergoes acceleration (changes velocity and direction) will emit electromagnetic radiation, losing energy in the process. A revolving electron would certainly transform the atom into a miniature radio station, the power output of which would be in ~ the price of the potential power of the electron; according to classic mechanics, the electron would just spiral into the nucleus and also the atom would certainly collapse. Figure $$\PageIndex2$$: The classical death spiral of one electron roughly a nucleus.

## Quantum concept to the Rescue!

By the 1920"s, it ended up being clear the a tiny object such as the electron can not be treated together a classic particle having a identify position and velocity. The finest we have the right to do is specify the probability that its manifesting itself at any point in space. If you had actually a magic camera that can take a sequence of pictures of the electron in the 1s orbit of a hydrogen atom, and could combine the resulting dots in a solitary image, you would watch something choose this. Clearly, the electron is an ext likely to be found the closer we relocate toward the nucleus.

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## Probability density vs. Radial probability

We can, however, talk around where the electron has the highest possible probability that manifesting itself— that is, wherein the maximum negative charge will certainly be found.

the motion of electrons can be predicted precisely.
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