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What are the heights of the electron orbits of an atom? (How far apart are the energy levels of the electron relative to the center of the atomic nucleus?) How fast do electrons move in their orbits?

Nick Stauner
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Robotex
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1 Answers1

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In the (incorrect) Bohr model of the hydrogen atom, for the ground state (n=1), the distance of the electron from the nucleus is 52.9 picometers (pm). The constant $a_0$ is defined to be this distance. The distance of the electron in the nth energy level is $a_0n^2$.

According to the exact solution of the Schrodinger equation for the hydrogen atom, in the ground state:

  1. $a_0$ (52.9pm) is the most probable distance of the electron from the nucleus.

  2. There is a 0.323 probability that the electron is closer than $a_0$, 0.677 probabilty that it is further away.

  3. The average distance of the electron from the nucleus is $\frac{3}{2}a_0$

  4. The probability that the electron is between r and r + dr from the nucleus is:

$$ \frac{4}{a_0}r^2e^{-\frac{2r}{a_0}}dr$$

Concerning velocity, the Heisenberg uncertain principle implies that given the knowledge that the electron is confined in its position to the degree explained above, the uncertainty in speed is on the order of $10^7 m/s$.

DavePhD
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