Quantum (Haehner) Flashcards
equation for frequency?
v = dE/h
what energies can v possess (looking at particle character of EM radiation)
0, hv, 2hv…
what is p in the de broglie equation?
linear momentum
what is the de broglie equation?
[lambda] = h/p
how do diffraction patters arise?
from many waves interfering constructively and destructively
what is h bar?
h/2pi - planck’s constant which takes angular momentum into consideration
general schrodinger equation?
HY=EY
what is the schrodinger equation for a particle in a 1D box?
-(hbar^2/2m)*(d^2[psi]/dx^2) + V(x)[psi] = E[psi]
give some examples of observables
momentum, energy, position
what is the position operator?
x[bar]=x*…
what is the momentum operator?
p[bar]x = h(bar)/i*d/dx…
What is the Born interpretation?
gives the probability of finding a particle between x and xdx
what is the equation for probability density?
|[psi]x|^2
what is the expectation value?
the average value of a large number of observations
3 steps to forming a schrodinger equation?
1) write down the total energy in terms of kinetic and potential
2) replace momentum and position in the energy equation with appropriate operators
3) then solve the SE to obtain eigenstates and eigenvalues.
What is a polar coordinate?
A 2D system of coordinates where all points are referenced off a central point by distance and angle
What symmetry does potential energy in the schrodinger equation have?
centrosymmetric
What can polar coordinates do to the schrodinger equation?
split it into radial and angular components
What are spherical harmonics?
the normalised wave functions of the angle dependent part of the schrodinger equation.
What is a hydrogen atom?
an atom or ion with only 1 electron
What is the equation for the Coulomb interaction of an electron with a nucleus?
V(r) = - Ze^2 / 4[pi][eo]r
What is the equation for the eigenvalues for the hydrogen atom?
En = -Z^2[mu]e^4 / 32[pi]^2[eo]^2h(bar)^2n^2
What is a boundary surface?
the area in which you are most likely to find an electron in an orbital - the shape of the orbital
What is the Born-Oppenheimer approximation?
oscillations from e- arrangement to equilibrium position moves faster than nuclei –> so the wavefunction can be separated into smaller components
How does the potential energy curve differ upon observation?
observed has a deeper well
What symmetry does a diatomic wave function need to have?
antisymmetric
in an antisymmetric function, when the sign of psi changes, what happens to the sign of fermions and bosons?
fermions change sign, bosons retain sign
What does valence band theory not account for?
lone pairs (when calculating angles) or hybridisation
What is the schrodinger for the hydrogen molecule ion H2+?
-h(bar)/2me (triangle)^2 + V
If you solve the schrodinger for a molecule what can you make?
attain 1 e- wave functions called MOs
How do you normalize a wavefunction?
Put N, a normalisation factor in front, which gives the probability of finding the particle in space equal to one
What is it called when an e- can be found in an atomic orbital belonging to atoms A and B in a wavefunction?
an LCAO
What does the potential energy curve describe?
the accumulation of e- density in and out of the internuclear region.
What do two orbitals need to have in common to form an orbital
symmetry
In which diatomic elements does sp mixing occur?
How do you measure bond order?
1/2(number of e- in bonding orbitals - number of e- in anti bonding orbitals)
Why is oxygen paramagnetic?
its a triplet state
What is a coefficient? (c)
it tells you how much each atomic orbital contributes to the overall MO
What is the variation principle?
If an arbitrary wavefunction is used to calculate the energy, the value calculated is never less than the true value.
It allows you to find optimum coefficients and energies.
How would you build an optimum molecular orbital?
start with a trial wavefunction then vary the coefficients until the lowest energy is achieved.
What is [alpha]? in the energy expression
the coulomb integral
what is [beta]? in the energy expression
the resonance integral
what is S? in the energy expression
the overlap integral
What is the coulomb integral?
the sum of the potential energy an electron feels from interacting with the charge distribution of a different electron
How do you find the minimum value for energy?
set dE/dc=0 (then find roots to obtain values for coefficients)
Once you know the minimum value for energy, what other things can you find out?
coefficients and total wavefunction (or MO)
In a heteronuclear diatomic, when the energy difference is large, how do the energies of the MOs differ from AOs?
only differ slightly - implies that bonding and anti bonding effects are small.
What is the Hückel approximation?
that sigma and pi bonds should be treated differently - sigma provides shape of the molecule.
How does a computational equation work?
Looking for a minimum energy value
find derivative of energy; use variation principle; find non trivial solution determinant=/=0; polynomial then use E values for find coefficients.
What is the equation for moments of inertia?
I = sum of mr^2
What are the four types of rigid rotors? (and what are their moments?)
linear (1 moment), spherical (3 equal moments), symmetric (two equal moments), asymmetric (3 different moments)
What is the equation for the classical energy of a body rotating about a?
Ea = 1/2 Ia*wa^2
what is the equation for angular momentum around axis a?
Ja = Ia*wa
What is the energy of a rotational energy level (including the angular mometum)?
E = Ja^2/2Ia + Jb^2/2Ib + Jc^2/2Ic
What is the quantum expression for energy of a spherical rotor?
Ej = J(J+1) * h(bar)^2/2I
What is B?
rotational constant = h(bar)/4pic*I