Week 2
Recitation Section 1
1. How are the units of energy and charge related?
E=CV=J;
2. The Rydberg constant of 13.6 eV. What is it in cm-1 and J?
c, 2.997925 x 108 m s-1 ; h, 6.6262 x 10-34 J s; e, 1.6022 x 10-19 C (Note that 1 eV = 1.6 022×
10-19 J Why is the conversion of eV to J just the charge on the electron? and 1 cm-1 =
h " c "10 2 = 1.602 "10#23 J )
3.
!
When you shine light on a metal you can sometimes get electron to come off of
the metal. The figure below shows the number of electrons observed as you
change the frequency of light.
a. Can you explain why the number of electrons is 0 for frequencies less
then ν0 and constant above ν0?
b. Why when you increase the light intensity does the number of electrons
observed increase?
c. Can you write an equation for the energy of the electrons that are emitted
in terms of the energy of the light?
d. Draw a graph of the kinetic energy of the electrons vs frequency of the
incident light.
Note that for a photon the energy is given by: E=hν. Thus, as we increase the frequency of
the light the energy of the photon increases. However, to remove an electron from a metal
you must have a least a minimum energy to overcome the binding energy of the electron to
the metal surface. When the frequency is very low the energy of the photon is not enough
to remove an electron from the metal. As we increase the frequency of the light (and the
energy of the photon) it will at some point, v0, have enough energy to just overcome the
binding energy of the electron to the metal and it will then remove an electron from the
metal. As the frequency increases more you will not get more electrons since one photo
will yield at most one electron. Thus as the energy of the photon increased you get the
same number of electrons however each electron will have more energy. Thus the number
of electrons stays constant however the energy of the electron that comes off get higher.
When you increase the light intensity but do not change the frequency you are not
changing the energy of the photons, rather you are increasing the number of photons.
Thus if you are at a frequency above the threshold you will get more electrons coming off
since one photon will yield one electron.
4. We can write the uncertainty relationship for position and momentum as
"x"p > h 2 . We know that E = p 2 2m . What is the relationship between the
uncertainty in p and E. (hint take the derivative).
5.
!
For the Bohr atom show that the radius of an orbit is inversely related to the
square of the velocity.
!
We know that
Ze 2
v2
Ze 2
=
m
r
=
which
when
you
rearrange
you
get
4 "#0 r 2
r
4 "#0 mv 2
6. How much energy is required to ionize the last electron in B?
!
E = 13.6 * Z 2!12 = 13.6 * 25 = 340eV
!
7. From the Bohr angular momentum requirement you can derive that: r = nh mv .
Does this agree with your answer in question 7.
This relation ship is not only between r and v since there is n in the equation. In order for
r to change both n and v must also change. Thus it does not contradict the above answer
!
since it is a relationship between three variables not two.
8.
What is the energy of 900 nm light in J, cm-1 and eV.
(2.21×10-19J, 1.11×104 cm-1, 1.38 eV)
9. A Ru complex absorbs light at 450 nm and emits light at 600 nm. What is the
energy difference between the absorbed and emitted light? (5.55×103 cm-1)
10. Under ordinary light levels, then molecules emit light they almost always do it at
a wavelength longer than the one they absorb light at. Why? (Conservation of energy
requires that the absorbed energy plus the energy of the atom must be equal to the emitted energy
and the atom after it emits. Thus if the atom is in its lowest energy state at the beginning the most
energy that can come out is equal to the absorbed energy if the atom ends in its ground state, if the
atoms end up in an excited state the light then comes out must be less then what went in.
11. If a H atom absorbs a photon of wavelength 90 nm what happens to the atom?
(13.8 eV it ionizes)
12. When an H atom goes from n=3 to n=1 how much energy does it need and what is
the wavelength of the light? Is the light emitted or absorbed? (9.75×10-6 cm-1, emit
102 nm)
13. Which of the waves below are standing waves? How many nodes do the standing
waves have?
14. An atom absorbed green light of wavelength about 500nm. It is in it's excited
state for a very short time and then emits light between 600.0 and 602.0 nm.
What is the uncertainty of the excited state energy level? What is the lifetime of
the excited state?
1 1e7nm
E green =
= 2e4 cm-1
500nm cm
1
1e7 nm
E 600 =
= 1.6667e4 cm-1
600.0nm cm
!
!
1
1e7 nm
= 1.6611e4 cm-1
602.0 nm cm
E 600 " E 602 = 56 cm-1
Converting to Joules we get
56 h J sec c cm
"E =
#
= 56 # (6.626e $ 34 ) # (2.998e10) = 1.11e $ 21 J
cm
sec
E 602 =
!
!
"t"E >
!
"t >
!
!
h
2
h
1.054e # 34 J sec
1
=
= 4.7e #14 sec
-1
cm
2"E
2 $ 56 cm
h J sec c
sec