PHYSICS
1310
Quiz 9 - Quantum Applications
Key
1. The electronic configuration of carbon (Z = 6) is 1s2 2s2 2p2. What is the electronic configuration for
the following atoms?
a. oxygen (Z = 8) 1s2 2s2 2p4
c. aluminum (Z = 13) 1s2 2s2 2p6 3s2 3p1
2. For the states of a hydrogen atom, write down the orbital magnetic quantum numbers and spin
quantum numbers corresponding to all possible quantum states with the principal quantum number equal
to 3 and the orbital quantum number equal to 1.
n = 3 and l = 1  ml = -1, 0, +1 and mS = - ½ and +½
How many states are there?
6
3. The ionization energy of carbon is 11.3 eV. Calculate the wavelength of the longest wavelength
photon that will ionize carbon.
 = 1240 nm-eV / 11.3 eV = 110 eV
4. In a container of hydrogen gas at 1982 K, there are 1.00 x 106 atoms in each of the states with n = 2.
a. How many hydrogen atoms are in each of the states with n = 3?
n3 / n2 = exp[-1.89 eV / (8.617x10-5 eV/K *1982K)] = 16 x 10-6  n3 = 16 atoms
b. How many hydrogen atoms are in all of the states with n = 3?
n3states = 18 * 16 atoms = 288 atoms;
note: n2states = 8.00 x 106 atoms
5. In a photovoltaic cell, every incident photon is absorbed and creates an electron that contributes to
the cell current. Suppose a square 1.0 mm x 1.0 mm PV cell is fully irradiated by a 5.0 mm diameter
laser beam with intensity equal to 2.0 x 107 W/m2 and wavelength equal to 620 nm.
a. Calculate the power absorbed by the cell, expressed as J/s. P = 20 J/s
b. Calculate the photon energy, expressed as J. Eph = 2.0 eV = 3.2 x 10-19 J/photon
c. Calculate the number of photons absorption rate, expressed as number of photons / s.
rate of photon absorption = P/Eph = 6.25 x 1019 photons / s
d. Calculate the rate at which electrons are generated, expressed as electrons / s.
rate of electron generation = rate of photon absorption = 6.25 x 1019 electrons / s
e. Express your answer to d as a photocurrent in Amperes.
(Recall that 1 A = 1 C / s and that e = 1.6 x 10-19 C.)
I = 6.25 x 1019 electrons / s x 1.6 x 10-19 C / electron = 10 C/s = 10 A