Probability of finding electron inside bohr radius

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Homework Statement


Consider an hydrogen atom in its ground state, what is the probability that the electron is found inside the Bohr Radius?


Homework Equations



The probability of finding the electron at bohr radius is maximum. but the probability over the range from 0 to bohr radius, is hard to visualize.

The Attempt at a Solution



http://www.physics.uc.edu/~sitko/CollegePhysicsIII/28-AtomicPhysics/AtomicPhysics_files/image024.jpg
graphically, the probability is area under the curve from 0 to bohr radius, but how to do it mathematically?
 

Answers and Replies

  • #2
gabbagabbahey
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Hint: The area under the curve [itex]f(x)[/itex] between [itex]x_0[/itex] and [itex]x_1[/itex] is

[tex]\int_{x_0}^{x_1} f(x)dx[/tex]
 
  • #3
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Hint: The area under the curve [itex]f(x)[/itex] between [itex]x_0[/itex] and [itex]x_1[/itex] is

[tex]\int_{x_0}^{x_1} f(x)dx[/tex]
i know this, is a calculus. but the real things is how to represent the wavefunction of hydrogen atom?

[tex]Probability=\int\psi*\psi dx[/tex]
 
  • #4
gabbagabbahey
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The ground state wavefunction for a hydrogen atom is computed (at least approximately) in every introductory QM text I've seen....surely you've come across it before?
 
  • #5
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The ground state wavefunction for a hydrogen atom is computed (at least approximately) in every introductory QM text I've seen....surely you've come across it before?
alright then, will flip through it, in case i miss out. thanks. by the way, i should be working in spherical coordinate right?
 
  • #6
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ok, that would be [tex]\psi_{100}=\frac{1}{\sqrt{\pi a^{3}}e^{\frac{-r}{a}}[/tex]
bingo!


[itex]\psi_{100}=\frac{1}{\sqrt{\pi a^{3}}e^{\frac{-r}{a}}[/itex]
 
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