Unit 7

Question 1

s orbital

Answer 1

-Nondegenerate atomic orbitals with angular momentum quantum number l=0
-spherically shaped
-# of orbitals in subshell=1
-spherically symmetric around nucleus
-value of wave function depends only on r
-2s and 3s have nodes (where wave function value is 0)

Question 2

contour

Answer 2

-used to represent the electron density distribution of a molecule
-when shading electron density, shading is greatest at ψ2 and must fade to white at nodes
-identify points at which ψ takes on 0.05, 0.1, 0.3, 0.5, 0.7, and 0.9 of its maximum value

Question 3

nodal contour

Answer 3

where the amplitude of the wave function is zero

Question 4

radial probability density

Answer 4

the probability density of finding the electron at any point in space at a distance from the nucleus, after integrating over all angles φ and θ
-r^2[Rn0(r)]^2
-small near nucleus, reaches max at distance where electron is most likely to be found

Question 5

angle φ

Answer 5

runs from 0 to 2π (on xy plane)

Question 6

angle θ

Answer 6

runs from 0 to π (on z plane)

Question 7

the size of an atom

Answer 7

-the wave function of an electron in an atom stretches out to infinity, so an atom has no clear boundary
-the size of an atom is the extent of “balloon skin” inside which 90% of the probability density of the electron is contained
-size of orbital increases with increasing n

Question 8

p orbital

Answer 8

-A set of three degenerate atomic orbitals with angular momentum quantum number l=1
-dumbbell shape
-have 3 angular wavefunctions with l=1, allowed m values are m= -1, 0, 1, leading to 3 orbitals with different orientations

Question 9

angular wave function

Answer 9

-function that describes the angular distribution of an electron around a nucleus, depending on the spherical coordinates (θ, ϕ)
-has separate lobes with positive and negative phases with nodes between them
-independent of r and n
-determines shape and names of orbitals

Question 10

angular node

Answer 10

-a surface in a wave function at which the electron density equals zero across which the wave function changes sign
-AN=l
-to find AN, set cos/sin of AWF to 0 and solve for θ/ϕ

Question 11

number of radial nodes in Rnl waves functions

Answer 11

n-l-1

Question 12

d orbital

Answer 12

-Atomic orbitals for which the angular momentum quantum number l=2
-four-leaf clover shaped
-maximum amplitude is at 45°
-each d orbital has 2 angular nodes

Question 13

important features for orbital shapes and sizes

Answer 13

-for a given l, an increase in n leads to an increase in the average distance of the electron from the nucleus and therefore the size of the orbital
-an orbital with quantum numbers n and l has l angular nodes and n-l-1 radial nodes (giving total of n-1 nodes)
-energy depends only on the number of nodes (n)
-as r approaches 0, ψ(r,θ, ϕ) vanishes for all orbitals except s orbitals
-thus, only electrons in s orbital can penetrate the nucleus (have a finite finite possibility density)

Question 14

size of an orbital (rnl)

Answer 14

-the average value of the distance of the electron from the nucleus in that orbital
-(n^2a0/Z)(1 + 1/2[1- l(l+1)/n^2])

Question 15

dz^2

Answer 15

m=0, has max amplitude along z axis, has a little “doughnut” in xy plane

Question 16

Drawing 3D standing waves

Answer 16

-for s orbitals, orbitals lie halfway between outside of next orbital and nucleus (outermost portion of standing wave has much larger volume than inner regions)

Question 17

radial node

Answer 17

-a sphere about the nucleus on which ψ and ψ2 are zero
-the more numerous the nodes in an orbital, the higher the energy of the corresponding quantum state of the atom
-RN= n-l-1