The wave function for hydrogen in the 1s state may be expressed as $\psi(r) = Ae^{-r/a_0}$, where $A = \frac{1}{\sqrt{\pi a_0^3}}$. Determine the probability for locating the electron between $r = 0$ and $r = a_0$.
Added by John L.
Close
Step 1
The wave function must satisfy the condition that the integral of the square of the wave function over all space is equal to 1. ∫ |Ψ|^2 dV = 1 For the 1s state of hydrogen, the wave function is given by Ψ = Ae^(-o). So, we need to calculate the integral of |Ψ|^2 Show more…
Show all steps
Your feedback will help us improve your experience
Krystal K and 79 other Physics 103 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 wave function for hydrogen in the 1s state may be expressed as ψ(r) = Ae^(-r/a0), where A = 1/√(πa0^3). For the case where N = 0.720, determine the following. (a) Determine the probability for locating the electron between the nucleus r = 0 and r = Na0. (b) Determine the probability for locating the electron between r = Na0 and r = ∞.
Timothy J.
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.
Recommended Textbooks
University Physics with Modern Physics
Physics: Principles with Applications
Fundamentals of Physics
Watch the video solution with this free unlock.
EMAIL
PASSWORD