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Challenge problem:
A common question asked by newcomers to the quantum structure of the atom is: “What keeps the
electron from falling into the nucleus?”
Time for a challenge!
One way to understand the origin of this effect is to focus on the implications of the Heisenberg
Uncertainly Principle (HUP), which states that confining a particle over a region
∆
X necessarily gives
rise to an uncertainty in the momentum,
∆
P = h/4 π
∆
X, where h is Planck’s constant.
In the case of very
low energy levels, we can consider the
∆
P to be a crude estimate of the available P values, since P has to
be at least as big as
∆
P.
In that case,
P
∼
h/4π
∆
X.
Now consider how the energy of an electron that is confined by the Coulomb potential around a nucleus,
U(r) = Ze
2
/4πε
o
r.
There are two contributions to the total energy, as always, one from the kinetic and the
other from the potential energy of the particle.
Our strategy is to combine the two contributions to show
that E depends on the r value of an electron trapped by the turning points, r
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This note was uploaded on 01/10/2011 for the course CHEM 100 taught by Professor Johnson during the Spring '10 term at NYU.
 Spring '10
 Johnson
 Electron, Nucleus

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