The wave function for an electron in a hydrogen atom is ? = Ne^(-r/a?). Here, r is the distance from the distance from the nucleus to the electron and a? is Bohr radius. Calculate the normalization factor, N. (A) (?a?)¹?² (B) (1/?a?³)¹?² (C) (?/a?³)¹?² (D) (1/?a?³)²
Added by Jeff C.
Close
Step 1
We are given a wave function for an electron in a hydrogen atom, which is expressed as Ψ = Ne^(-r/a), where r is the distance from the nucleus to the electron, a is the Bohr radius, and N is the normalization factor we need to find. The normalization condition for Show more…
Show all steps
Your feedback will help us improve your experience
Timothy James and 72 other Physics 101 Mechanics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
The ground-state wave function for the electron in a hydrogen atom is $$\psi_{1 s}(r)=\frac{1}{\sqrt{\pi a_{0}^{3}}} e^{-r / a_{0}}$$ where $r$ is the radial coordinate of the electron and $a_{0}$ is the Bohr radius. (a) Show that the wave function as given is normalized. (b) Find the probability of locating the electron between $r_{1}=a_{0} / 2$ and $r_{2}=3 a_{0} / 2$.
The wave function for the 1s state of an electron in the hydrogen atom is ψs (r) = Ae^(-r/a0) where a0 is the Bohr radius. The probability of finding the electron in region W of R' is equal to ∫∫∫|ψs (r)|^2 dV, where in spherical coordinates, ψs (r) = (1/πa0^3)^(1/2) e^(-r/a0). Use integration in spherical coordinates to show that the probability of finding the electron at a distance greater than the Bohr radius is equal to 1 - (1 + r/a0) e^(-2r/a0).
Shaiju T.
The normalized radial wave function for hydrogen in the n = 1 state is given by R1s (r) = e^(-r/aB) where aB is the Bohr radius. The probability to find the atom's electron in a spherical shell bounded by aB/2 < r < aB is given by: (need to know the angular momentum quantum numbers (l,m))
Jacob F.
Recommended Textbooks
University Physics with Modern Physics
Physics: Principles with Applications
Fundamentals of Physics
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD