Bohr Model: Explaining Why Electrons Don't Enter Nucleus

[ConceptuallyInept]

I liked the Bohr model as it explained why the electrons aren't sucked into the nucleus. (Balancing of centipetal and centrifugal forces). Am I right in saying that the electrons still orbit the nucleus to avoid electrostatic attraction except we can't make very accurate judgements about the way it does this because of the wave-nature of the electron and its obedience to wave mechanics and Heisenburgs UP?

Thanks

 

[misogynisticfeminist]

not really, electrons cannot be seen as little balls, they are clouds around the nucleus. And you don't find clouds moving in circular motion. The thing is that the electron wavefunctions obey HUP, and therefore won't get sucked into the nucleus. HUP is the answer, not circular motion.

 

[DaveC426913]

Actually, it's even less straightforward than that. Electrons are not clouds around the nucleus. The cloud is merely a representation of the probability that, when observed, the electron will be found at a given point.

 

[misogynisticfeminist]

if they're not clouds, then what are they? The probability which the electrons have being at particular points are not a lack of information, but they are the electron. Isn't this probability something physical ? (not the wavefunction which is physical, but the probabilities of the particle being found at different places at one time).

 

[James Jackson]

The wavefunction isn't physical - remember it's describe by complex quantities. What is a physically representable property is the wavefunction (in position representation) squared, which gives the probability of finding the particle in a certain point in space (or describes your 'cloud' if you like). What is also 'physical' is information you can get from the system at a given time (I forget the orginator, but the quote 'Information in Physical' applies here!).

These other 'physical' quantities result from measurements on the wavefunction. For example, the momentum operator is $\hat p = -i\hbar\nabla$, and the position operator is $\hat x = x$. You perform a measurement of the operator on a wavefunction and the wavefunction then collapses to the eigenvector corresponding to the eigenvalue you measured. Note in the momentum and position case, these eigenvectors / values form a continuous spectrum, as oppoed to, say, a measurement of spin.

So, how much 'physical' information can we get out of a system? This is where the HUP plays a role (well, really where it's derived from). There is a function on operators (well, actually it's another operator) called the commutator, defined as [A,B] = AB - BA. If this doesn't equal 0, then the two operators can't be measured together to arbitary precision. From working out expectation values of measurements on $\hat p$ and $\hat x$ the HUP can be derived.

Note as an interesting 'side effect' / property of operators that do commute (and therefore can be measured together) - they share the same eigenspace.

So, the wavefunction is abstract, but we can get physical information by measuring operators on it.