Consider the wavefunction of a hydrogenic atom: (r, theta,) = 1/81 squarerootof
ID: 999747 • Letter: C
Question
Consider the wavefunction of a hydrogenic atom: (r, theta,) = 1/81 squarerootof pi (z/a)^7/2 (r^2 exp-Ar/3a)) (3 cos^3 theta -1) were a is a constant. Can the above wavefunction penetrate into the center of the nucleus? (Yes or No) Are there any radial nodes? (Yes or No) If yes, determine the location(s) of the radial nodes. How many angular nodes are in this wavefunction? (0, 1, 2, or 3) Determine their angles if there is any angular node. Which of the following hydrogenic atoms has a greater probability of finding its electron at r = 0.01 nm from the center of the nucleus (about r = 0.2a) and theta = 0 degree for the above wavefunciton: (r, theta,) 1/81squrerootof6pi(z/a)^7/2 exp(Zr/3a)(3 cos^2 theta -1), (Be^3+ or Li^2+ or same for both or others) Explain your choice. Determine the most probable distance in terms of a for the above wavefuction of hydrogen atom (Z = 1) (r, theta,) 1/81squrerootof6pi(z/a)^7/2 exp(-r/3a)(3 cos^2 theta -1)Explanation / Answer
Hydrogenic wave function contains two parts.one is radial one and the other part is the angular part. We can determine many things by this equation. Few examples are the type and the shape of orbitals and nodes.
Radial nodes = n-1 where n= total no.if orbitals.
e ^ -Zr/3a. By the coefficient of a we can find n. Here n=3
So radial node = n-1 = 2