Download Atomic Line Spectra: the Bohr model Line Spectra of Excited Atoms

Atomic Line Spectra:
the Bohr model
Niels Bohr’s great contribution to science
was in building a simple model of the
atom. It was based on observations of
the SHARP LINE SPECTRA of
excited atoms.
• Excited atoms emit
light of only certain
wavelengths
• The wavelengths of
emitted light depend
on the element.
See screen 7.6 on the CD-ROM
Feb. 22, 2006
Line Spectra
of Excited Atoms
High E
Short λ
High ν
Low E
Long λ
Low ν
Visible lines in the H atom spectrum
are called the BALMER series.
See jersey.uoregon.edu/vlab/elements/Elements.html for
an interactive line spectrum periodic table.
Feb. 22, 2006
Page 1
Atomic
Atomic Spectra
Spectra and
and Bohr
Bohr
One (incorrect) view of atomic structure in
early 20th century was that an electron (e-)
traveled about the nucleus in an orbit.
+
Feb. 22, 2006
Electron
orbit
That view:
1. Any orbit should be possible and so
should any energy.
2. But a charged particle moving in a
circle should emit energy.
The end result should be destruction!
Atomic
Atomic Spectra
Spectra and
and Bohr
Bohr
Bohr said that this classical view was wrong.
He saw the need for a new theory — now called
QUANTUM or WAVE MECHANICS.
–An e- can only exist in certain discrete orbits —
called stationary states.
–An e- is restricted to QUANTIZED (discrete)
energy states.
–The energy of a state = - (Rhc)/n2 = - (const)/n2
where n = quantum no. = 1, 2, 3, 4, .… and the
constants R = 1.1×107 m-1, h = 6.6×10-34 J·sec and
c = 3.0 ×108 m/sec
Feb. 22, 2006
Page 2
Atomic
Atomic Spectra
Spectra and
and Bohr
Bohr
Energy of a quantized state = - Rhc/n2
• Only orbits where n = integer number
are permitted.
• Radius of allowed orbits = 0.0529·n2 nm
• Results can be used to explain atomic
spectra, at least for simple atoms.
Feb. 22, 2006
Atomic
Atomic Spectra
Spectra and
and Bohr
Bohr
If e-’s are in quantized energy
states, then ∆E between states
can have only certain values.
This explains sharp line spectra.
E = -Rhc (1/2 2 )
n=2
E = -Rhc (1/12 )
n=1
See CD-ROM screen 7.7
See www.colorado.edu/physics/2000
Feb. 22, 2006
Page 3
Atomic
Atomic
Spectra
Spectra
and
and Bohr
Bohr
E = -Rhc (1/22 )
n=2
2
= -Rhc (1/1 )
n=1
E
N
E
R
G
YE
Calculate ∆E for e- “falling” from higher energy
level (n = 2) to lower energy level (n = 1).
∆E = Efinal - Einitial = -Rhc[(1/12) - (1/2)2]
∆E = -(3/4)Rhc
The atom’s final energy is less than its initial
energy, thus the atom is losing energy.
Feb. 22, 2006
Atomic
Atomic
Spectra
Spectra
and
and Bohr
Bohr
E = -C (1/22 )
n=2
2
= -C (1/1 )
n=1
E
N
E
R
G
YE
∆E = -(3/4)Rhc
The values of R, the Rydberg constant, h, the Planck
constant and c are known from experiment.
Rhc = 2.179×10-18 J/atom
so, E of emitted light = (3/4)Rhc = 1.63×10-18 J. This
corresponds to a frequency ν = E/h of 2.47 × 1015
sec-1 and λ = c/ν = 121.6 nm.
This is exactly in agreement with experiment!
Feb. 22, 2006
Page 4
Atomic
Atomic
Spectra
Spectra
and
and Bohr
Bohr
Bohr received the Nobel Prize
in 1922 for his theory.
However, there are problems —
• theory is successful only
for H.
• quantum idea artificially
introduced.
• So, we go on to QUANTUM
or WAVE MECHANICS to
understand the atom
Feb. 22, 2006
Quantum or Wave Mechanics
de
de Broglie
Broglie (1924)
(1924) proposed
proposed that
that
all
moving
objects
have
wave
all moving objects have wave
properties.
properties.
For
For electrons
electrons orbiting
orbiting aa nucleus,
nucleus,
he
he theorized
theorized that
that aa standing
standing
wave
is
set
up
in
each
wave is set up in each orbit.
orbit.
Because
Because each
each orbit
orbit has
has aa
predicted
predicted radius,
radius, the
the
wavelength
of
a
moving
wavelength of a moving particle
particle
is
λ
=
h/mv
(v
is
velocity).
is λ = h/mv (v is velocity).
Feb. 22, 2006
Page 5
This is the
quantum
part
This is the
mechanics
part
Quantum or Wave Mechanics
Baseball (115 g) at 100 mph:
λ = h/mv = (6.6×10-34 J·sec) /
[(0.115 kg) (45 m/sec)] =
1.3×10-34 m = 1.3×10-25 nm
Experimental proof of wave
properties of electrons
see CD-ROM screen 7.8
e- with velocity of 1.9 × 108
cm/sec:
λ = 3.88×10-10 m = 0.388 nm
Feb. 22, 2006
Quantum or Wave Mechanics
Schrödinger
applied the idea
of an e- behaving
as a wave to the
problem of
electrons in
atoms.
He developed what
is called the
WAVE
EQUATION
The solution to the wave
equation gives a set of
mathematical expressions
called
WAVE FUNCTIONS, Ψ
Each describes an allowed
energy state of an eQuantization comes naturally
from the mathematics.
Feb. 22, 2006
Page 6