1. How does the probability density
look like at the nucleus?
(A) There is a maximum at the nucleus for s-electrons, but it is zero for ℓ > 0 electrons with ℓ > 0 (p,d,f, etc.)
(B) There is a maximum at the nucleus for all orbitals
(C) The probability density is zero at the nucleus.

2. How does the probability density
look like at the nucleus?
(A) There is a maximum at the nucleus
for s-electrons, but it is zero
for ℓ > 0 electrons with ℓ > 0
(p,d,f, etc.)
(B) There is a maximum at the nucleus
for all orbitals
(C) The probability density is zero
at the nucleus.
... because of the factor r2 in the
above expression (r = 0 at the
nucleus). This makes sense,
because the Coulomb interaction
energy of the electron and the
nucleus would be infinitely large,
which would be unphysical.

3. Consider the orbitals and radial functions shown below. From the
shape of the orbitals and the radial functions, try to develop an
educated guess about the number of nodes in a H wave function. 2s
2pz
n-1 radial, ℓ-1 angular
(B) n-ℓ radial, ℓ angular
(C) n-ℓ-1 radial, ℓ angular
(D) n-1 radial, ℓ angular

4. Consider the orbitals and radial functions shown below. From the
shape of the orbitals and the radial functions, try to develop an
educated guess about the number of nodes in a H wave function. 2s
2pz
n-1 radial, ℓ-1 angular
(B) n-ℓ radial, ℓ angular
(C) n-ℓ-1 radial, ℓ angular
(D) n-1 radial, ℓ angular