# Probability of finding electron inside bohr radius

## 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?

gabbagabbahey
Homework Helper
Gold Member
Hint: The area under the curve $f(x)$ between $x_0$ and $x_1$ is

$$\int_{x_0}^{x_1} f(x)dx$$

Hint: The area under the curve $f(x)$ between $x_0$ and $x_1$ is

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

$$Probability=\int\psi*\psi dx$$

gabbagabbahey
Homework Helper
Gold Member
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?

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?

ok, that would be $$\psi_{100}=\frac{1}{\sqrt{\pi a^{3}}e^{\frac{-r}{a}}$$
bingo!

$\psi_{100}=\frac{1}{\sqrt{\pi a^{3}}e^{\frac{-r}{a}}$

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