1. The major consequences of the exclusion principle involves
a.Anti –parallel spins
b.lower energy orbital
c.orbital occupancy
d.higher energy orbital
2. The arrangement of elements in the modern periodic table based on their ____________
a.Increasing atomic mass in the period
b.Increasing atomic number in the horizontal rows
c.Increasing atomic number in the vertical columns
d.Increasing atomic mass in the group
Answers
Explanation:
B Fermi Gas Method
According to Pauli's exclusion principle, all electrons of the same spin orientation in a system must possess momenta that differ from each other by the amount specified above. The momenta of all electrons are completely fixed if it is further required that the system exist in its ground state, which is the lowest possible energy state for the system because there is just one way that this can be accomplished, which is for the electrons to occupy all the low-momentum quantum states before they occupy any of the high-momentum quantum states. In other words, there exists a fixed momentum magnitude pF and, in the ground-state configuration, all states with momentum magnitudes below pF are occupied while the others with momentum magnitudes above pF are unoccupied. Graphically, the momenta of the occupied states plotted in a three-dimensional momentum space appear like a solid sphere centered about the point of zero momentum. The summation of all occupied quantum states is equivalent to finding the volume of the sphere, since all states are equally spaced from each other inside the sphere. Let the radius of the sphere be given by pF called the Fermi momentum, then the integral for the volume of the sphere with the momentum variable expressed in the spherical polar coordinates is given by:
(4)∫
pF
0
4πp2dp=(
4π
3
)p
3
F
where p is the magnitude of p, p = ∣p∣. The number of electrons accommodated in this situation is obtained by dividing the above momentum volume by h3/V and then multiplying by 2, which is to account for electrons with two different spin orientations. The result is proportional to the volume V which appears because the total number of electrons in the system is sought. The volume V is divided out if the electron number density is evaluated, which is given by:
(5)ne=(8π/3h3)p
3
F
Equation (5) may be viewed as a relation connecting the electron number density ne to the Fermi momentum pF. Henceforth, pF will be employed as an independent variable in establishing the physical properties of the system.
The total kinetic energy density (energy per unit volume) of the electrons can be found by summing the kinetic energies of all occupied states and then dividing by the volume. Each state of momentum p possesses a kinetic energy of p2/2me, where me is the electron mass, and the expression for the electron kinetic energy density is
(6)ɛe=
2
h3
∫
pF
0
4πp2dp
p2
2me
=
2π
5h3me
p
5
F
ɛ
The average kinetic energy per electron is obtained by dividing ɛe by ne:
(7)ɛe/ne=0.6(p
2
F
/2me)