Quantum Mechanics

Question 1

Quantum chemistry and its application to spectroscopy

Answer 1

Classical experiments
Principle of quantum mechanics
Molecular orbital theory
Molecular spectroscopy

Question 2

Black body radiation

Answer 2

Thermal electromagnetic radiation within or surrounding a body in thermodynamic equilibrium with its environment, or emitted by a blackbody

Question 3

Radiant excitance

Answer 3

Glowing radiation caused by the heating up a a material i.e. Tungsten filament

Question 4

Blackbody

Answer 4

A perfect absorber that is a substance that absorbs all frequencies of light and emits none; it would be black

Question 5

Quanta

Answer 5

Discrete units of light energy; the energy of a quantum was directly proportional to a frequency of an oscillator; E = hv

Question 6

Photoelectric effect

Answer 6

e- are mutter from a metal when the metal is irradiated with visible/ UV radiation

Question 7

Photoelectric effect 1st observation

Answer 7

Below a given cutoff frequency of incident radiation, no e- were ejected from the metal surface, no matter how intense the radiation

Question 8

Photoelectric effect 2nd observation

Answer 8

Above the cutoff frequency, the # of e- emitted was directly proportional to the intensity of the radiation

Question 9

Photoelectric effect 3rd observation

Answer 9

As the frequency of the incident radiation increased, the maximum velocity of the ejected e- increased

Question 10

Photons

Answer 10

Light particles

Question 11

Einsteins Equation for photoelectric effect

Answer 11

ha = 1/2•mv^2 + w,
w = working energy,
1/2•mv^2 = kinetic energy of emitted electron

Question 12

Dual nature of radiation

Answer 12

Light can be both a particle and a wave; wavelength = h/p = h/mv,
p = momentum, h = Planck’s constant

Question 13

Planck’s constant

Answer 13

6.626x10^-34 J/s

Question 14

Heisenberg uncertainty principle

Answer 14

It is impossible to simultaneously measure the momentum and position of a particle such as an e-, because performing one measurement would disturb the particle and prevent the accurate measurement of the 2nd quantity

Question 15

Heisenberg uncertainty principle expression

Answer 15

dq•dp > h/4pi; the product of the uncertainty of the position (dq) and the uncertainty of the momentum (dp) is greater than h/4pi

Question 16

Principles of quantum mechanics

Answer 16

Has 5 postulates

Question 17

1st postulate of quantum mechanics

Answer 17

The physical state of a particle can be fully described by a wave function of type x,y,z,t

Question 18

2nd postulate of quantum mechanics

Answer 18

The x,y,z,t wave functions are obtained by solving the appropriate schrodinger equation.

Question 19

Shrodinger equation: for time-independent systems

Answer 19

h^2/8pim• 💎^2¥ + [E-V(r)]¥ =0,
💎= laplacian operator in units m^-2
V = potential energy
¥ = position-space wave function m^-3/2
E = energy in J
h = Planck's constant
M = mass in kg

Question 20

3rd postulate of quantum mechanics

Answer 20

Every dynamic variable that correlates with a physically observable property is expressed as a linear operator

Question 21

4th postulate of quantum mechanics

Answer 21

Operators that represent physical properties are derived from the classical expressions for these properties

Question 22

5th postulate of quantum mechanics

Answer 22

The eigenvalues obtained by solving the appropriate schrodinger equation represent all possible values of an individual measurement of the quantity in question

Question 23

Operators

Answer 23

Represented with a circumflex accent over the symbol that represents the variable in interest

Question 24

Shrodinger equation

Answer 24

A complex wave function used to describe the quantum mechanical state of a particle

Question 25

Probability density (w)

Answer 25

The probability of finding a particle at time t at a give position r = x,y,z in a volume dV; w = |¥|^2dV

Question 26

Time-dependent wave function

Answer 26

Used to describe the harmonic wave motion of a free particle

Question 27

Time dependent wave function

Answer 27

``` ¥(r,t) = (a)e^i[wt-(k•r)]; a = amplitude in units of m^-3/2 i = imaginary unit =(sqrt(-1)) w = frequency k= wave number vector r = radius vector describing the position of the particle in space ```

Question 28

Eigenfunctions

Answer 28

Solutions to the schrodinger equation, and they exists only for specific eigenvalues of energy

Question 29

Eigenvalues

Answer 29

The totality of them for E yields the tire energy spectrum of the particle

Question 30

Harmonic oscillator

Answer 30

A particle that has mass m which, under the influence of a linearly applied force, will move in one or several directions with a frequency of w0

Question 31

Schrodinger equation for one-dimensional harmonic oscillator

Answer 31

d^2¥/dx^2 + 8pim/h^2•[E-(mw0^2/2)x^2]¥ = 0

Question 32

Zero point energy

Answer 32

The lowest energy possible for the harmonic oscillator

Question 33

Harmonic oscillator is used to model:

Answer 33

The vibrations of atoms and molecules | The lattice vibrations of crystalline materials