Prince George’s Community College
CHM
1010(Shah)
Chapter 7: The quantum mechanical atom
Outlines:

Electromagnetic radiation – as a wave or a stream of photons

Atomic line spectra

Properties of electrons: particles and waves

Quantum theory
Wavelength: unit is generally in meter, nm, Å (1 Å = 10-10m)
Frequency: Unit is per second (s-1) means Hz
Speed of light (c )= 3.00 x 108m.s-1
c = λ x ν (wavelength x frequency)
1.
What is the frequency of 254nm wavelength? (1.18 x 1015 Hz)
2.
What is the wavelength of 1240kHz radio waves? (242m)
Energy of photon (a single quantum): Ephoton =h x ν
where h is a Plank’s constant = 6.626 x 10-34 J.s
1.
What is the energy of the one photon of the microwave radiation at
1.20cm wavelength? (1.66 x 10-23J)
2.
calculate the energy of one photon of ultraviolet (λ = 1 x 10-8m), visible
light(λ = 5 x 10-7), and infrared (λ = 1 x 10-4m) light.
3.
Calculate the energy of one photon of yellow light of 589nm in joule.
Convert this in joule/mol.
Atomic spectra:
Rydberg equation 1/λ = RH(1/n12 – 1/n22)
n2 > n 1
Rydberg constant RH = 2.18 x 1018J for hydrogen
For the hydrogen atom, the energy of an electron in an orbital with
quantum number n is given by the following equation.
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En = -2.18 x 1018J(1/n2)
1.
The lines in the visible portion of the hydrogen spectrum are called Balmer
series, for which n1 = 2 in the Rydberg equation. Calculate to four
significant figure, the wavelength in nanometers of the spectral line in this
series for which n2 = 4. (2.0565 x 104 cm-1) (486.3nm)
2.
Calculate the wavelength in micrometers, µm, of radiation expected when
n1 = 4 and n2 = 6.
de-Broglie’s equation:
λ = h/mv
1.
or
λ = h/mu
where v or u is speed.
Calculate de-Broglie’s wavelength of an electron with a speed of 1.00 x
106m/s. electron mass =9.11 x 10-31kg, h= 6.626x10-34 J.s or 6.626x10-34
kg.m2/s (7.27 x 10-10m)
2.
What is the speed of an electron that has a de-Broglie wavelength of
100nm?
3.
How fast must a 56.5g tennis ball travel in order to have a de-Broglie
wavelength that is equal to that of a photon of green light(5400 Å)?
The wave that corresponds to the electron is called a wave function. The wave
function is usually represented by the symbol (ψ) and known as orbital. It can be
used to describe the shape of the electron wave (orbital) and its energy.
Quantum theory:
2
The principle quantum number (n): The quantum number n is called the principle
quantum number, and all orbitals that have the same value of n are said to be in
the same shell. The value of n can range from n = 1 to n = α .

As n increases the energy of orbital increases.

The higher the value of n, the larger is the electron’s average distance
from the nucleus.
The secondary quantum number (the orbital angular momentum quantum
number)(l). The angular quantum number(l ) divides the shell into smaller groups
of orbitals called subshells.( l = n -1). The value of l determines the name of the
subshell.
The electron spin gives us a fourth quantum number for the electron, called the
spin quantum number ms. Which can take two possible values ms = + ½ or
ms = - ½
Shell (subshell)
(label)
# of orbitals (2l +1) (# of orbitals x 2)
n
(l )
name
in subshell
1
0
s
1
2
2
1
p
3
6
3
2
d
5
10
4
3
f
7
14
maximum electrons
The magnetic quantum number,ml: The third quantum number is known as the
magnetic quantum number. Its value indicates individual orbitals within a
subshell. The range from +l, to – l.
1.
How many subshells are in shell number 4 (n =4)? Give the label of these
subshells? How many orbitals are in each of these subshells?
3
Shell n = 4, subshells
l=
One 4s,
five 4d,
three 4p,
0,1,2,3 , orbitals: 4s,4p,4d,4f
seven 4f
How many total orbitals are in shell n = 4?
total 16
How many total orbitals are in subshell (l) = 3?
7
How many total electrons are in shell n = 4?
32
Hint: use n2 formula for total orbitals in shell and use 2(l) + 1 formula for
the number of orbitals in each subshell. For maximum number of electrons
in shell use 2n2 formula.
2.
Give the name, magnetic quantum numbers, and number of orbitals for
each sublevel with the given quantum numbers.
(a) n = 3, l = 2 (b) n = 2, l = 0 (c) n = 5, l =1 (d) n = 4, l = 3
n
l
Sublevel
Possible ml values
name
3.
3
2
2
0
5
1
4
3
3d
N0. Of orbitals
In subshell
-2,-1, 0, +1, +2
5
Supply the missing quantum numbers and sublevel name.
n
L
ml values name
?
?
0
4p
2
1
0
?
4
4.
3
2
-2
?
?
?
?
2s
What is wrong in each of the following quantum number designations
and/or sublevel name?
n l
5.
ml values name
1
1
0
1p
4
3
+1
4d
3
1
-2
3p
Which of the following electron transitions corresponds to absorption of
energy and which to emission?
(a)
6.
n = 2 to n =4 (b)
n = 3 to n = 1
(c) n = 5 to n =1
How many orbitals in an atom can have each of the following
designations?
a.
7.
1s
b.
4d
c.
3p
d.
n = 3 e.
n =2, l = 1
How many maximum electrons can have for n = 3?
Paramagnetic and diamagnetic: Unpaired electron (all attracted to the magnet)
indicated in an orbital diagram is known as paramagnetic and paired (not all
attracted to the magnet) indicated in an orbital diagram is known as diamagnetic.
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