GR0177 #93



Alternate Solutions 
radicaltyro 20061028 23:38:14  One can also note that this is more or less the definition of the bohr radius.  

Comments 
UNKNOWNUMBER 20181020 23:28:34  I think this is one of those problems ETS expects you to know the answer to by heart after taking a quantum class.   bhaynor 20091003 12:30:22  I get C. It asks for the most probable value of r, not the expectation value of r. The most probable value of r occurs when Psi is maximized, at r = 0.
bhaynor 20091003 12:32:07 
Ignore my last comment. I forgot about r^2.

  anmuhich 20090317 13:09:47  You can also remember that in general lower energy states are more probable and that the lowest energy state of hydrogen is the ground state at the bohr radius.   Imperate 20081004 14:52:04  An interesting note on this question, is that the most probable value of r for the ground state wavefunction, is NOT equal to the expectation value.rnrnThe expectation value is actually 1.5a_o.rnrnhttp://hyperphysics.phyastr.gsu.edu/hbase/quantum/hydr.html#c3rnrnshows nice solutions to both of these related problemsrnrn   radicaltyro 20061028 23:38:14  One can also note that this is more or less the definition of the bohr radius.
mitama 20080809 17:56:58 
Depending on the wavefunction, this may or may not be true (luckily, in this case it is). It's probably best to go through the work just to be sure.

syrock 20091008 16:50:41 
yeah, hydrogen.... bohr.... come on its gatta be a0

Almno10 20101110 19:56:42 
I don't think this is the definition of the bohr radius. The bohr model is classical.
The "come one, its bohr" argument is correct. The bohr model is very good despite its crappy, classical derivation.

walczyk 20110407 20:55:37 
Almno10: The brilliant thing about bohr is that he reached this result with his own protoquantum mechanics, and thus the radius is named after him. go read a book

walczyk 20110407 20:56:55 
nvm, read it wrong and didn't mean to post a dick comment :/

  jax 20051130 19:03:20  Why does dV become ? Isn't that the surface area ?
yosun 20051130 20:19:06 
jax: thanks for the typo alert; the typo's been fixed: . (The radial probability distribution is related to the probability by .)

 




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