Reference no: EM131041167
1. a. How many radial nodes arc present in the radial eigenfunction associated with the 2p atomic orbital for hydrogen-like systems? What about the number of nodes in the corresponding spherical harmonics?
b. For the hydrogen-like Mercury ion (Min, at what values of r will the radial nodes appear?
Note: R21(r) = {1 / 4(6)1/2}{Z/aa}3/2 ρe-ρ/4
Where ρ = 2Zr / aa
2. Using the atomic wavefunctions given in class and in your textbook, plot BY HAND the probable location of the electron contained in the 2p] orbital of a hydrogen atom on the graph below. Explain with the help of equations, how you achieved this plot?
3. The normalized eigenfunctions for a particular hydrogen-like atom whose radius is Ro are
Ψ(r, θ, Φ) = Rn1(r) Y11(θ, Φ) for r ≤R0
and Ψ(r, θ, Φ) = 0 for r>R0
Y11(θ, Φ) is a spherical harmonic equal to (3/8 π)1/2 sin θei θ, and Rn0(r) = (2/R0)1/2[(sin [nπr/R0])/R0]
What is the average radial position of the particle as a function of the quantum number n.
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