CH101 SPRING 2012 MID TERM REVIEW QUESTIONS (CHAPTERS 1-3) SOLUTIONS
1. A modification of the de Broglie matter wave equation that accounts for the presence of
potential energy is
h
λ(r) =
2m[ E  V (r )]
Calculate the de Broglie wavelength in Å for an electron in helium (assume 4.00 amu for the
He nucleus) at a fixed total energy E of − 3.40 eV at a distance of 2.0 Å from the nucleus.
Electron-electron repulsion may be ignored.
[Planck’s constant h = 6.626 x 10-34 Js; mass of electron m = 9.109 x 10-31 kg]
V (eV )  14.40

q1q2
2 1
 14.40
 14.40 eV  2.3110 18 J
r
2.0
6.626 1034 J  s
2  (9.109 10
31
kg )  (3.40  (1.602 10
19
J )  2.3110
18
 3.75 1010 m
J)
3.75 Å or 0.375 nm
2. Determine the wavelength of the first line in the emission spectrum of H in the Paschen
series (based on n = 3).
[RH (Rydberg constant) = 3.29 x 1015 /s; c (speed of light) = 3.00 x 108 m/s]
The Paschen series is the one based on n = 3 and the first line (the one of longest
wavelength) in the emission spectrum is formed by n4  n3.
1
 (/s) = R (/s)
_
n32
= 3.29 x 1015 (/s)
1
n42
1 _ 1
9
16
= 1.599 x 1014 /s
Since  = c/ ,  = (3.00 x 108 m/s) / (1.599 x 1014 /s)
= 1.88 x 10-6 m or 1880 nm
3. Determine the maximum wavelength of light that is needed to eject electrons from the
surface of sodium, if the work function of sodium is 4.41 x 10-19 J.
[Planck’s constant h = 6.626 x 10-34 Js; speed of light c = 2.998 x 108 m/s]
The maximum wavelength of light here is the one that supplies just enough
energy to overcome the work function ( ) at the surface of Na. The electron
kinetic energy here is zero and hence, from the Einstein equation, E = 
6.626 x 10-34 (Js) x 2.998 x 108 (m/s)
E =  = hc Hence,  =

4.41 x 10-19 (J)
= 4.50 x 10-7 m or 450 nm (visible region)
4. Identify and sketch the boundary surface for the orbital with the following wave function:

1
=
81 6 
a0
_ 3
2
 = r/a0, where a0 is the Bohr radius.
2
e
_ 
3
(3cos2  - 1)
5. Sketch the plot of radial distribution function (r 2[R(r)]2) versus r for 1s, 2p, 3d and 4f
orbitals, relating the value of r for the maximum value of the function with a0, the Bohr radius.
6. Give n, l, number of orbitals, number of radial nodes and number of angular nodes for the
orbitals, 3s, 2p, 6d, 5f and 5p.
Orbital
3s
2p
6d
5f
5p
n
l
3
2
6
5
5
0
1
2
3
1
No. orbitals
1
3
5
7
3
No. radial nodes
2
0
3
1
3
No. angular nodes
0
1
2
3
1
7. Predict which of the following pairs of ions have the greatest coulombic attraction in a solid
compound
(a) K+, O2- : Ga3+, O2- ; Ca2+, O2(b) Mg2+, S2- ; Mg2+, Se2- ; Mg2+ O2(a) K, Ca and Ga are all in the 4th period. Ga3+ is smallest and most highly charged cation
and so forms the strongest coulombic attraction with O2-.
(b) O, S and Se are all in group VIA, with O 2- being the smallest anion. Hence coullombic
attaction is greatest for Mg2+ O2-.
8. Write the best Lewis diagram for the anion PO2Cl2-.
P is central atom (group VA)
.. _
:O :
..
: Cl
..
P
+
..
:O
..
..
..
: Cl
..
Cl :
..
P
: O: _
..
Cl :
..
: O: _
..
(With fewer formal charges)
9. Write down Lewis diagrams, with formal charges on all atoms, for the molecules cyanic
acid (HOCN) and fulminic acid (HCNO). State which molecule is likely to be the more stable.
Lewis diagrams (with all formal charges):
0
0
0
0
0
+
0
0
..
..
..
..
H
O
C
N
H
C
N
O
or
H
C
:
..
..
HOCN can be written with no formal charges and hence is more stable
+
N
0
..
O:
10. Write resonance structures for the formate ion (HCOO -) and comment on the C-O bond
length in real formate salts.
..
.... _
O:
O
.. :
H
C
H
.. _
C
O
.. :
O:
..
O
H
C
_
O
Resonance implies
equal C-O bond
lengths (agrees with
experiment)
11. Arrange the following in order of bond strength.
(a) HCl; HF; HBr; HI
(b) O2; F2; N2
(a) The order of atomic size is F<Cl<Br<I, hence order of bond strength is HF>HCl>HBr>HI.
(b) Bond orders are O2 = 2; F2 = 1; N2 = 3, hence order of bond strength is F2<O2<N2.
12. Use the VSEPR theory to determine the shape of the tellurium tetrachloride (TeCl4)
molecule. State whether TeCl4 is polar or nonpolar.
..
: Cl :
..
: Cl
..
Lewis diagram
xx
Te
: Cl :
..
..
Cl :
..
electron pairs = 5: trigonal bipyramidal arrangement,
Cl
Cl
:
but “seesaw” or “distorted tetrahedron” shape
Te
Cl
Cl
polar
13. Use the Valence bond theory to sketch the molecule ketene (CH2=C=O), showing
hybridization modes of C and O, types of sigma bonds, and pi bond formation.
14. Sketch molecular orbital diagrams for the following species, and arrange them in order of
increasing bond order. BC, OF-, N2-, NO+, BN.
15. Sketch the molecular orbital energy diagram for NH and predict its magnetic properties.
16. Use MO theory to predict which of the following has the strongest bond: NO +, N2+, O2+.
Identify and sketch the MO boundary surface of the NO+ highest occupied MO (HOMO).