8.6 The Shapes of Atomic Orbitals

probability density

probability (per unit volume) of finding the electron at a point in space

s orbitals

spherically symmetrical

radial distribution function

mathematical function (corresponding to a specific orbital). that represents the total probability of finding an electron within a thin spherical shell at a distance r from the nucleus

radial distribution

The _________________________ function represents, not probability density at a point r, but total probability at a radius r.

0

In contrast to probability density, which has a maximum at the nucleus, the radial distribution function has a value of _ at the nucleus.

probability density function and volume of the thin shell

The shape of the radial distribution function is the result of multiplying together two functions with opposite trends in r:

greatest

In the quantum-mechanical model, you would generally find the electron at various radii, with 52.9 pm having the _________ (least/greatest) probability.

node

2s and 3s orbitals are larger in size than the 1s orbital, and unlike the 1s orbital, they contain at least one ____.

node

a point where the wave function, and therefore the probability density and radial distribution function, all go through zero

0

The probability of finding the electron at a node is _.

p orbitals

not spherically symmetric like s orbitals, have two lobes of electron density on either side of the nucleus and a node located at the nucleus

orientation

The three p orbitals differ only in their ___________ (size/shape/orientation) and are orthogonal (mutually perpendicular to one another).

nodes, larger

The orbitals of same angular momentum quantum number (l) but increasing principal quantum number (n) are all similar in shape, but they contain additional _____ (like the higher s orbitals) and are progressively ______ (smaller/larger) in size.

p_x orbital

two lobes of electron density along the x axis

p_y orbital

two lobes of electron density along the y axis

p_z orbital

two lobes of electron density along the z axis

d orbitals

• four have clover leaf shape with four lobes of electron density around the nucleus and two perpendicular nodal planes

• d_z² orbital has two lobes oriented along the z-axis and a donut-shaped ring around the xy plane

d_yz orbital

4 lobes of electron density oriented along the yz plane

d_xy orbital

4 lobes of electron density oriented along the xy plane

d_xz orbital

4 lobes of electron density oriented along the xz plane

d_x²-y² orbital

4 lobes of electron density oriented along the x and y axes (2 lobes each)

d_z² orbital

two lobes oriented along the z-axis, donut-shaped ring along the xy plane

f orbitals

7 orbitals with more lobes and nodes than d orbitals

nodal plane

plane where electron probability density is 0

phase

with regard to waves and orbitals, the sign of the amplitude of the wave, which can be positive or negative

same, opposite

When orbitals interact, their wave functions may be in phase, ____ (same/opposite) sign, or out of phase, ________ (same/opposite) sign

orbitals

The roughly spherical shape of an atom is obtained by superimposing all of its _______.