Ch 4!!! Fundamentals of Quantum Mechanics

Question 1

two observations that scienctists in the end of 19th century just couldn’t understand

Answer 1

1. atoms, when inserted in flame, emit light of certain (and not any) colour
   2.heated objects (such as a frying pan) emit light of particular colours, these change with temperatures

Question 2

how does quantum theory help us

Answer 2

most complete theory we have to describe the behaviour of electrons, in turn explains how many biological, physical, and chemical processes work. ex, electronic devices rely on quantum mechanical nature of electrons

Question 3

diffraction

Answer 3

the bending of waves by an obstacle

Question 4

interference

Answer 4

property of all waves, waves interfere with each other and themselves either constructively or destructively

diffraction generally produces concentric circles

Question 5

concentric circles

Answer 5

circles with a common center, in the case of waves this would be the origin

Question 6

how does diffraction occur

Answer 6

as each wave/electron/particle hits atom in crystal lattice, wave splits and it’s components interfere with each other NOT with other electrons

Question 7

momentum

Answer 7

mass x velocity

Question 8

wavelength

Answer 8

distance between nearest points repeating pattern (trough to trough)

Question 9

de broglie’s equation

Answer 9

fancy upside down y h thing = h/p. and p = mv

when fancy thing = wavelength (m)
p = momentum of the particle. kg m s^-1
m = mass of particle in kg
v = velocity of particle in m s^-1. or m/s
h = planck’s constant (6.626 x 10^-34 Js

Question 10

why can we detect wavelike behaviour in electrons etc, not larger particles like tennis balls??

Answer 10

due to the value of h being so small, if you were to divide it by the velocity of a large object you would get a wavelength immensely smaller than the volume of the object being observed. Because of this larger particles do not exhibit observable wavelike properties

Question 11

how can you maximize diffraction of particles

Answer 11

wavelength should be the same as spacing in lattice etc they will be passing through. If smaller than, diffraction will not occur and if greater than, each particle will be diffracted by many atoms etc and the diffraction pattern will be blurred

Question 12

travelling waves

Answer 12

repeating and periodic disturbances that travel from one location to another

Question 13

what do waves transport??

Answer 13

ENERGY not matter, energy that disturbs still medium. Electromagnetic ration transmits energy through oscillating electric and magnetic fields

Question 14

Definition of a Transverse Wave, how can they be represented??

Answer 14

wave which oscillates in direction perpendicular to direction of motion

Amplitude, Wavelength, Frequency

the waves intensity and energy are proportional to the square of it’s amplitude

Question 15

waves intensity and energy proportional to ___

Answer 15

the square of it’s amplitude

Question 16

amplitude

Answer 16

difference between midpoint and crest or trough

Question 17

wavelength

Answer 17

length of one complete cycle, crest to crest or trough to trough

Question 18

frequency

Answer 18

complete cycles the wave can transmit per unit time

Question 19

speed of wave

Answer 19

velocity, unit of distance divided by unit of time

velocity in m s^-1 = frequency (italic v, in s^-1 or Hertz) x wavelength (fancy h y in meters)

Question 20

EQUATIONS TO KNOW

Answer 20

velocity (v) = frequency (italic v) x wavelength

wavelength in m= h(planck’s constant) Js / momentum of a particle in kg m s^-1

Kinetic energy = 1/2 m v^2

momentum in kg m s^-1 = mass of particle (kg) x velocity of particle in m s^-1

E = h^2 n^2 / (8mL^2)

change in energy = h^2 / 8mL^2 x (Ef^2 - Einitial^2)

Question 21

what happens to the wavelength of a particle when velocity decreases

Answer 21

as velocity decreases, momentum decreases and thus wavelength increases

Question 22

basic sin function of a wave

Answer 22

f(x) = Asin (2pix/wavelength)

A is a constant, amplitude

Question 23

standing wave

Answer 23

bound on either side (length L), appear to be still and do not carry energy from one place to another

Question 24

how can standing wave be formed

Answer 24

travelling waves of equal amplitude and frequency but in opposite directions interfere with each other

Question 25

nodes

Answer 25

points where amplitude = 0, generally where waves deconstructively interfere with each other

Question 26

where is particle on a wave??

Answer 26

it can exist simultaneously everywhere, position can only be predicted - PROBABILITY

Question 27

heisenberg uncertainty principle

Answer 27

we cannot know precisely (with zero uncertainty) both the position and momentum of a microscopic particle at the same time

Question 28

particle at rest, velocity momemtum annd KE?

Answer 28

all equal to zero

Question 29

probability distribution of particle in a box

Answer 29

uniform across length of box, and equal to 1/L

Question 30

remember when predicting average momentum

Answer 30

momentum is a VECTOR both magnitude and direction

Question 31

psi (fancy wierd greek y)

Answer 31

WAVEFUNCTION - all info that can possibly be obtained from a quantum system in a given state

Question 32

probability distribution of a wave??

Answer 32

find by taking the square of the wavefunction

Question 33

schrodinger equation

Answer 33

not even going to try to type, google

Question 34

what does potential energy describe

Answer 34

ex hydrogen atom n, electron moving in coulomb field of proton, v is PE of the electron from coulombic force between nucleus and electron

PE (V) will depend on the problem

Question 35

schrodinger for particle in a box

Answer 35

-h^2/ 8pi^2m x d^2/dx^2 psi = Epsi

d^2/dx^2 psi just means the derivative of the wavefunction

Question 36

wavefunction for quantum particle in a box

Answer 36

psi = Asin (kx)

COMPLETE

psi = √(2/L) sin ((npix)/L)

Question 37

n

Answer 37

principle quantum number, must equal a positive integer number

Question 38

why can’t n be a fraction?

Answer 38

with quantum particle in a box function, psi must equal 0 at L, sin (kL) = 0, this only happens at sin(npi), therefore n can only be a positive integer

Question 39

value of amplitude quantum particle in a box

Answer 39

√(2/L)

Question 40

where is the maximum of probability graph?

Answer 40

if amplitute psi = √2/L amplitude of wavefunction equals square of this

ex if L = 1 amplitude of prob graph is 2

Question 41

how do you known # of nodes in quantum particle in a box??

Answer 41

n - 1

Question 42

equation for energy of particle in a box

Answer 42

E = h^2 n^2 / (8mL2)

Question 43

ground state

Answer 43

E1 = h^2 / 8mL^2.

LOWEST possible energy

always greater than 0

Question 44

zero point energy

Answer 44

difference between the ground state energy and zero

Question 45

excited state

Answer 45

any state n>1, so 2, 3, to infinity

n=2 is first excited state

Question 46

how can particles change their energy levels

Answer 46

absorbing or emitting energy, ex recieve energy from light or from collisions

Question 47

equation change in energy level

Answer 47

change in E = E final - E initial

E final energy of the system in final state (nfinal)

E initial, initial energy original n

change in E = h^2/(8mL^2) x (nfinal^2 -ninitial^2

Question 48

what does change in energy level mean?

Answer 48

if positive, system absorbed energy

if negative, system emit energy

Question 49

can particle gain lose completely random amounts of energy??

Answer 49

no, quantized, quantum system never observed between states, can only gain or lose exact amounts of energy

Question 50

determining n, wavelength, function (psi), and probability distribution function given # of nodes

Answer 50

n = # of nodes + 1

wavelength = 2L/n

function = √(2/L) sin ((n pi x)/L)

probability distribution function = 2/l sin^2((n pi x) /L)

Question 51

how to calculate any excited energy state

Answer 51

calculate ground state using h^2 / 8mL^2

multiply this by n^2

Question 52

quantized

Answer 52

can only take on certain values