Probability of an electron's position (Quantum Mechanics)

[balthazar]

Homework Statement

If a Hydrogen atom is in it's ground state - calculate the probability that the electron will be found within 10^-14m of the nucleus. The nucleus can be assumed to be point like.

Homework Equations

∫〖x^2 e^(-x/a) dx〗=-e^(-x/a) [ax^2+2a^2 x+2a^3 ]+constant

 

[arkajad]

Take the ground state - you should have the formula. Make sure it is normalized (when integrated over r form 0 to infinity should give 1, do not forget integrating over the angles). Calculate the integral of the probability density from 0 to 10^-14m (do not forget about the angles).