Solutions to example questions in Lect-01 Handout.
(ex)
"Radio 78: has a carrier frequency of 780 kc. What is the wavelength of this frequency?
3
780 kc = 780 x 10 sec
(ex)
λ=
1-
3x108 m / sec
780x103 sec− 1
= 385meters
Chicago street lights commonly use sodium vapor lamps. The wavelength of the emitted
radiation (involving sodium valence electrons) is 589 nm. What is the corresponding frequency
and energy of this radiation?
3x10+ 17 nm / sec
υ=
=
589 nm
5.093 x 10
+14
sec
-1
E( photon) = (6.626x10− 34 J ⋅ sec)(5.093x10+ 14 sec− 1) = 3.375 x 10 -19 Joules
E( mole) = (3375
. x10− 19 J / photon)(6.02x1023 photon / mole) = 203 kJ / mole
(ex)
Suppose an electron in H atom moved from the second shell (n=2) to the sixth (n = 6).
According to the Bohr expression, determine the frequency of radiation associated with this
process. Is this process exothermic or endothermic? What is the energy of a photon associated
with this process. What is the energy of this process for a mole of hydrogen atoms (or
equivalently, a mole of photons)? Does this radiation lie in the visible region of the
electromagnetic spectrum? In this radiation emitted or absorbed?
1
1
E = (−2178
. x10− 18 Joule / photon) 2 − 2  = 4.84 x 10 -19
6 2 
υ=
4.84x10− 19 Joule / photon
− 34
6.626x10
Joule⋅ sec
= 7.305 x 10
+14
sec
Joule/photon
-1
The electron moves further from the nucleus (from 2 to 6) so the process is endothermic.
E ( mole) = 291.4 kJ / mole
λ=
3x1017 nm / sec
+ 14
7.305x10
−1
= 410.7 nm
sec
This radiation lies in the visible spectrum in the blue range of colors.
(ex)
Suppose an electronic transition in H atom emitted radiation of 1283.445 nm and was the result of
an electron moving from the fifth shell. According to the Bohr expression, what is the quantum
number (value of n ) for the final target shell in this transition?
3x10+ 17 nm / sec
υ=
= 2.337459 x 10 +14
1283.445 nm
(note SEVEN significant figures. Use them.)
ALGEBRAIC SIGN of frequency must always be positive, but ENERGY is not so restricted.
This is an emission process, or EXOthermic, so sign of ENERGY is negative.
E( photon) = (6.626x10− 34 J ⋅ sec)(2.337459 x10+ 14 sec− 1) =
(ex)
- 1.548803 x 10
-19
J
 1 1
− 1548803
.
x10− 19 Joule = (−2178
. x10− 18 Joule / photon) 2 − 2 
n 5 
1
= 0.07111113 + 0.04 = 0.1111111
n2 = 8.999999 = 9
n( final ) = 3
2
n
According to eq. 4, what is the energy of the electron in hydrogen atom when n = ∞ ? What
label is given to the energy required to move a H atom electron from n = 1 to n = ∞ ?
with the electron in the n = ∞ energy level, the hydrogen atom is at the zero of energy.
for the transition from
n = 1 to n = ∞ , the energy is given by...
1
 1
E = (−2178
. x10− 18 Joule / photon) 2 − 2 
∞
1 
E( mole) = 1311 kJ / mole
= +2.178 x 10
-18
Joule / photon
Note, this is the ionization energy for hydrogen atom.
Or, in other words, the Rydberg constant is the ionization energy.
(ex)
?
What is the de Broglie wavelength of a ball of 100 g mass moving at 100 mph?
m
miles  1hour   1min   5280 ft   12in  1meter 
= 100
= 44.70 m
sec
hour  60 min  60sec  1mile   1 ft   39.37in 
6.626x10− 34 J ⋅ sec
λ=
(010
. kg)(44.70 m / sec)
= 1.482 x 10
-34
/ sec
meters
(At present there is no known device that can measure a distance this small. So it can not be
concluded that this moving object is without wave character, all that can be said is that it is not
detectable with present instrumentation.)
(ex)
What is the de Broglie wavelength of an electron moving at one-tenth the speed of light?
mass = 9.109 x 10
λ=
-31
kg
6.626x10− 34 J ⋅ sec
− 31
(9109
. x10
2.425 x 10
-11
8
= 2.425 x 10
-11
meters
kg)(0.3x10 m / sec)
meters = 0.2425 D and this wavelength can be detected.
This is high energy radiation - of the order of X-rays in energy.
Electron beams of this energy cause diffraction effects in crystalline materials, and diffraction is a
wave phenomena. So, we can (and do) conclude that moving matter has wave character; it's an
experimentally proven fact.
(ex)
Construct an energy level diagram showing (1) relative kinetic energy, (2) the wave function,
and (3) the wave function squared, all as a function of location along the length dimension from
=0 to
=a.
x
x
This will be worked-out in class.