Phy5646/hydrogen atom lifetime lifetime: Difference between revisions

Revision as of 16:00, 18 April 2010

Excited Hydrogen Atom Lifetime.

We start with the wavefunctions of the ground and first excited state of the hydrogen atom.

$\psi _{100}={\dfrac {e^{-r/a_{o}}}{\sqrt {\pi a_{o}^{3}}}}$

$\psi _{200}={\dfrac {e^{-r/2a_{o}}}{\sqrt {32\pi a_{o}^{3}}}}\left(2-{\dfrac {r}{a_{o}}}\right)$

$\psi _{210}={\dfrac {e^{-r/2a_{o}}}{\sqrt {32\pi a_{o}^{3}}}}\left({\dfrac {r}{a_{o}}}\right)cos(\theta )$

$\psi _{21\pm 1}={\dfrac {e^{-r/2a_{o}}}{\sqrt {64\pi a_{o}^{3}}}}\left({\dfrac {r}{a_{o}}}\right)sin(\theta )e^{\pm i\phi }$

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 '''Excited Hydrogen Atom Lifetime.'''
+We start with the wavefunctions of the ground and first excited state of the hydrogen atom.
+<math>\psi_{100}= \dfrac{e^{-r/a_o}}{\sqrt{\pi a_o^3}}</math>
+<math>\psi_{200}= \dfrac{e^{-r/2a_o}}{\sqrt{32\pi a_o^3}} \left( 2-\dfrac{r}{a_o} \right)</math>
+<math>\psi_{210}= \dfrac{e^{-r/2a_o}}{\sqrt{32\pi a_o^3}} \left( \dfrac{r}{a_o} \right) cos(\theta)</math>
+<math>\psi_{21 \pm 1}= \dfrac{e^{-r/2a_o}}{ \sqrt{64\pi a_o^3}} \left( \dfrac{r}{a_o} \right) sin(\theta) e^{\pm i \phi}</math>