Transcript Bohr Model and Principal Quantum Number

The Bohr Model and The
Principal Quantum Number
Physics 12 Adv
Absorption Spectra
 When white light (all visible
wavelengths) is incident upon a
gaseous sample of an element, an
absorption spectra will be produced
 These spectra provide valuable
insight into the structure of the
atom
Absorption Spectra
Various WL sources
 Since every element has a unique
absorption spectra, then if the light
from any source is analyzed, the
elements that comprise the source
can be determined
 Consider the following plot of
spectra from different sources:
4500
4000
Relitive intensity (arb units)
3500
3000
solar 1
2500
incandecent bulb
2000
flouresent blub
lcd white
1500
crt white
1000
500
0
-500
350
400
450
500
550
Wavelength (nm)
600
650
700
750
Balmer Series
 Balmer showed that
the visible lines
(656.3nm, 486.1nm,
434.1nm and
410.2nm) could be
predicted using:
 Verify that this is
correct
1 1
 R 2  2 

2 n 
n  3,4,5,...
1
R  1.09737315x107 m 1
Rydberg Equation
 Rydberg went on the show that all
hydrogen lines could be predicted
using:
1
1
 1
 R 2  2 

m n 
m, n  1,2,3,...
nm
 Use this to predict hydrogen
spectral lines for n and m values up
to 6
Hydrogen Spectral Lines
 Lyman
 Balmer

 122nm
 656nm
 103nm
 486nm
 97.2nm
 434nm
 94.9nm
 410nm
 93.7nm
Paschen

 1870nm
 1280nm
 1090nm 
Brackett
 4050nm
 2630nm
Pfund
 7460nm
Bohr Postulates
 Once he saw Balmer’s work, Bohr
developed his model
 Bohr postulated:
1. Electrons exist in circular orbits
2. Electrons exist only in allowed orbits
3. Electrons do not radiate energy within
an orbit
4. Electrons can jump between orbits
Principal Quantum Number
 Bohr’s model requires the use of the
principal Quantum Number (n)
 It predicts the line spectra of
hydrogen through the energy levels
of electron orbitals
 Unfortunately, Bohr’s model works
well for hydrogen but does not
completely predict other atoms
Angular Momentum
 Is a conserved vector quantity within
a system
 Similar to momentum, it involves the
mass of an object and velocity but
additionally, the radius through which
it moves
 Break down the units of Planck’s
Constant (Js) into standard units
 What does this tell us?
Quantized Angular Momentum?
 The units of Planck’s constant can be
broken down into kg, m and m/s which
would be the product of mass, distance and
velocity
 Angular momentum is the cross product of
radius and momentum so it is comprised of
the same units
 Bohr hypothesized that angular momentum
may be quantized which led to the following
equation:
nh
mvr 
2
 n
Two Key Equations
 Coulomb’s Law (Electrostatic Force)
kqQ
F 2
r
 Centripetal Force (Circular Motion)
mv
F
r
2
Setting Coulomb’s Law equal to the
centripetal force gives:
2
2
me v
ke

2
r
r
2
2
ke  me v r
2
ke
r
2
me v
If we solve Bohr’s quantized angular
momentum equation for velocity, we
see:
r
2
ke
 n 

me 
 me r 
2
2
 n 
2
  ke
rme 
 me r 
2
2
n
2
 ke
me r
2
2
n
rn 
2
me ke
Bohr Radius
 The previous equation can be solved
for any principal quantum number
you choose; check your answer by
solving for n = 1, 2
 r1=5.29x10-11m
 r2=2.12x10-10m
 These values agree well with the
known size of an atom ~10-10m
Section Review
 Page 876
 1-8