Question

Write down the wave functions (i) Ψ210 and (ii) Ψ300 for the hydrogen atom. Obtain the expectation value of r for the ground state hydrogen atom.

23 Jan 2025
Answer :
Word Count : 322
The wave functions for the hydrogen atom are given in terms of quantum numbers \( n \), \( l \), and \( m \). The normalized wave functions in spherical coordinates (\( r, \theta, \phi \)) are: \[ \Psi_{nlm}(r, \theta, \phi) = R_{nl}(r) Y_l^m(\theta, \phi) \] where \( R_{nl}(r) \) is the radial wave function and \( Y_l^m(\theta, \phi) \) is the spherical harmonic. ### (i) \( \Psi_{210} \) Wave Function For \( n = 2 \), \( l = ______ __________ ____ ____ _________ ___ ________ _____ __________ ___.
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