Download Problem Set 6 Solutions

Problem Set 6 Solutions
1.
a)
A hydrogen atom in a certain excited state has its electron in a 5f subshell. The electron drops
down to the 3d subshell, releasing a photon in the process.
For each of these subshells, give the n and l quantum numbers, and give the range of possible
ml quantum numbers.
5f: n = 5, l = 3, ml = –3, –2, –1, 0, 1, 2, 3
3d: n = 3, l = 2, ml = –2, –1, 0, 1, 2
b)
(3 points)
How many radial nodes and how many angular nodes does each of the orbitals in part (a) have?
The total number of nodes equals one less than the quantum number n. The number of angular
nodes equals the quantum number l:
5f: 1 radial and 3 angular.
3d: 0 radial and 2 angular.
(3 points)
c)
Determine the wavelength of light that would be emitted by this process.
1%
" 1
E = 2.18 × 10–18 J $ 2 ! 2 '
#5
3 &
(
)(
= –1.55 × 10–19 J
)
6.63 ! 10 "34 J # s 3.00 ! 10 8 m/s
hc
λ=
=
E
1.55 ! 10 "19 J
= 1.28 × 10–6 m , or 1282 nm
(3 points)
d)
The hydrogen atom now has a single electron in the 3d subshell. Calculate the energy (in
kJ/mol) required to ionize this (excited state) hydrogen atom. This is the energy required to
remove the electron completely from the atom.
1 &
# 1
E = 2.18 × 10–18 J % 2 ! 2 (
$3 " '
#19
2.42 "10
!
= 2.42 × 10–19 J
1 kJ
6.02 "10 23 atoms
J"
"
1000 J
1 mol
= 146 kJ/mol
(3 points)
2.
The photoelectric binding energy of cesium is 183.7 kJ/mol. Light having a wavelength of 2.4
× 10–7 m falls upon a cesium surface in an evacuated tube. Calculate the minimum deBroglie
wavelength of the emitted photoelectrons.
KEelectron
= Ephoton – Ebinding
(6.626 "10
#34
(2 " 9.109 "10
J $ s)
#31
2
)
(6.626 "10 J $ s)(3.00 "10 m/s) # &(183.7 kJ/mol " 1000 J "
1 mol
=
+
'
1 kJ
6.02 "10 atoms *
kg) %
(2.4 "10 m)
8
#34
2
Solve for λ = 6.79 × 10–10 m
23
#7
(3 points)
!
3.
For each of the following orbitals, provide a perspective sketch of the orbital in the Cartesian x,
y, z coordinate system. Determine the number of angular nodes and the number of radial nodes
in the orbital, and describe where those nodes fall. (For instance, the 2px orbital has an angular
node in the yz-plane.) (3 points for each one, 12 points total)
a)
1s
radial = 0, angular = 0
c)
3dx2-y2 radial = 0 , angular = 2
(two planes with z and halfway between x and y)
b)
3px radial = 1, angular = 1 (in yz-plane)
d)
3dxz
radial = 0, angular = 2
(in yz-plane and xy-plane)
4.
Write electron configurations and count the number of unpaired electrons in:
O, Si, Ni, I, Ir, Bi, Gd
O: [He]2s22p4
2 unpaired electrons
Si: [Ne]3s23p2
2 unpaired electrons
Ni: [Ar]4s23d8
2 unpaired electrons
I: [Kr]5s24d105p5
1 unpaired electron
Ir: [Xe]6s24f145d7
3 unpaired electrons
Bi: [Xe]6s24f145d106p3
3 unpaired electrons
Gd: [Xe]6s25d14f7
8 unpaired electrons
(3 points total)