1b + 2b Flashcards
F = ma meaning equation
net force = mass x acceleration
when we hit a ball we know the balls
momentum and position in the air
if we know amts position and momentum we can say we know its
trajectory!!
the lines that guess where an object is gonna fall!!
H Y = EY is the
schrodinger wave equation!!
bc an e- is so small, what does it not have and what does it have
bc its so small it doesnt have a trajectory
we say an e- has a wavefunction!
think of a wave when u shoot one out a gun,, think water ripples etc
increase in frequency means what in terms of energy
an increase in energy
theyre proportional!!
E=hvn meaning
energy of ‘n’ photons
h = planks constant
v = frequency
normally E=hv only gives the energy of 1 photon of light.
brighter light means whattt,, in terms of photons and energy
a brighter light means there are more photons
but each photon still has the original energy!!
aka the energy of the photon doesnt change and increase when the light gets brighter,, u just get more photons.
what does E=hv mean
it means energy is quantised
meaning its not random
how do we know energy in an atom is also quantised?
H2(g) + spark gives 2H+(g)
and this relaxes to give 2H(g)
when it relaxes,, it gives out a photon of light. THIS IS EMISSION SPEC,, WE CAN SEE ENERGY BETWEEN DIFF ENERGY LEVELS: needs to equal the gap to be absorbed and given back out.
rhydberg equation shows how energy levels are quantised,, what the equation
v = Rh (1/n.small.2 - 1/n.big.2)
what did bohr suggest
he suggested that there are orbits around the nuc and these are where e- stay.
he basically said they have a trajectory.
each orbit has a ‘quantum number’ = n
larger n = further from nuc
what did bohr suggest about energy
that energy is proportional to 1/n2
where n is the principle quantum number
bigger n = further from nucleus.
what is the bohr model limited to
it’s limited to H only
bc other atoms have multiple electrons which alter the amount of Z felt by the outer electrons
electrons have
wave particle duality
what did de broglie say
he said that all particles have a wavelength !!
wavelength = in terms of debrogles
h/mv
planks / mass x velocity. !!!
classical and quantum evidence for e- having wave particle duality
classical = real world = e- shot at Ni bounced off it
quantum = physics = e- bounced off like a wave : kinda ripples coming off the square drawing
a detector detected where the e- ended up.
the fact that when shot at Ni ,, e- bounced off like a wave,, tells us what
that they have wave particle duality.
that they can be diffracted,, like a wave.
like light forming a rainbow 🌈! and light is a wave.
taking the e- bouncing off the Ni as a wave,, what can we plot
we can plot E(or probability) against angle (theta)
which gives us a bunch of hills that increase at the middle then decrease.
the peaks = where there’s lots of e- at that angle
troughs = no e- at that angle
it confirms that wavelength = planks / mass and velocity.
proves bohr wrong = e- do acc behave as waves.
we can use the probability + angle graph to find the wavelength
units for the wavelength = planks / mv
planks = js
mass = kg
v = m/s
wavelength of a 1 kg brick going 10m/s
wavelength of an e- going 10^4 m/s
h/1 x 10 = wavelength = (6.6x10-35)
h/(9.1x10^-31)(1x10^4) = wavelength = (7.3x10^-8)
the electron has a much larger wavelength!! due to its small masssss
why do larger objects have a small wavelength
bc there’s a large difference between planks and it’s mass
why do smaller objects have a greater wavelength
bc their mass and planks constant are similar
describe the graph for the wave function against r + what this graph shows
shows = probability of finding an e- at a certain distance across the atom
it goes from 0,, goes up,, then goes down and passes 0,, then goes a bit more up but doesn’t go across the x axis.
lower probs when it’s below the x axis
0 probs when it’s on the x axis
high probability when it’s above the x axis.
how do we find wavefunction
we find the wavefunction by solving the schrödinger equation!!!!
HY=EY!!!!
what does Y tell us (wave-function)
tells us the probability of finding an e- in an atom (at a certain distance)
bc an e- is a quantum object,; what don’t we know
bc e- is a quantum object,, we dk it’s position or momentum!!!
larger wavelength as h and its mass is similar
change in position and change in momentum (p and q) should beeeee
equal or larger than (h.dash//h)
(h.dash = h/2n) where n = pi.
we go over this iabbbb!!!
if change in q aka change in position iss a really large number,, what does this mean
it means we can’t be sure about where it is.
there’s a large uncertainty as it could be right next to u,, or 60m away from u. so large position uncertainty.
what is a large position uncertainty normally due
it’s normally due to the massss
large mass = classical object
= small wavelength = large position uncertainty
H’ Y = EY is the + what are the different things
time independent schrödinger equation
H’ = hamiltonian operator.
Y = wavefunction.
E = energy of particles.
it relates wavefunction to the energies of the particles
H’ is the ,,, which meanssss
hamiltonian operator
operator means we want to separate the 1st derivative !! and low-key find the second one aswell.
how do we know if something is an eigen function
when the 1st derivative is a NUMBER X ORIGINAL FUNCTION!!!
aka the 1st derivative gives u a number infront of the original thing.
aka e^kx gives Ke^kx so yess it’s an eigen function
if the 1st derivative of e^kx is Ke^kx,, what is the eigen value
the eigen value is the number in front of the eigen function
aka it would be ‘K’ this time.
when ur done with checking if the 1st derivative is a eigen function and has an eigen value,, what else do u do
u do the same thing for the 2nd derivative
when something has an eigen value,, what else is the next requirement
has to fulfill the born requirements
born requirements
needs to be
normalised
finite
single valued
continuous
what does H’ do
the hamiltonian constant describes the energy of the particles + includes all the terms that contribute TO the particles energy
( potential and kinetic)
H’ is equal to
T’ + V’
kinetic energy + potential energy
bc it describes the energy of the particle including all the things that contribute to its energy
KE
= 1/2mv^2
p (momentum) =
mass x velocity
KE = in terms of momentum (p)
KE = p^2 /2m
which is approx involved with T’ (kinetic energy)
So what does T’ (kinetic energy) equal to =
T’ = (-h.dash^2 /2m ) (second derivative)
h.dash = h/2n
n= pi.
If H’ is the energy of the particle and so equals T’ + V’ ,, how else can we write the schrödinger equation
(T’ + V’)Y = EY
which hopefully gives us an eigen value
and if H’ = T’ + V’
and T’ = (-h.dash/2m)(second derivative) ,, how else can we write the schrödinger equation
[(-h.dash/2m)(second derivative) V’]Y = EY
this is for 1 particle,, of mass(m),, moving in one direction
if V’ (potential energy) is 0 due to the particle being a free particle
what does H’ equal
H’ = T’
meaning the energy of particle depends on its kinetic energy aka how much it moves.
if V’ is 0,, for a free particle,, how else can we write the schrödinger equation
T’ Y = EY
if a value with ‘a’ in it is an eigen function,, can the value of ‘a’ change if it is an eigen function or not??
nope!!!
the value of ‘a’ will not alter it it’s an eigen function or not!!
if a value with ‘a’ in it is an eigen function,, can the value of ‘a’ change if it is an eigen function or not??
nope!!!
the value of ‘a’ will not alter it it’s an eigen function or not!!
if the value ‘a’ is in an eigen function : and doesn’t alter if it’s an eigen function or not,, how and what does a small, mid and large a value change
low a : more relaxed wave,, broad peaks : low KE//low arrangement // 2nd derivative
mid a : more intense wave with larger peaks
high a: intense wave with large peaks: large KE // arrangement // 2nd derivative
in the sin wave there are regions of
positive and negative interphase !!
there’s also a bunch of sun waves that give that sin wave.
so the more we know about it’s position,, the less we know about it’s momentum!!
what do we do to find the probability of finding a particle between x and dx
Y^2 dx = Y
what’s the problem with plotting Y against r aka wavefunction against r
u can get a negative probability,, aka a negative wavefunction at a certain distance
what do we plot instead of Y against r
we plot Y^2 against r
this way we don’t get a negative probability : we can get nodes where it reaches the x axis or areas of high // low probability. never negative probability.
bc square of a negative is a positive.
Y^2 >_ 0
what is integration
area under a curve.
is equal to 1.
aka the probability of finding an e- here is 1!!
born requirements for graph of Y^2
normalised ( integration =1)
finite (keeps going forever)
single valued ( nice curve shape)
continuous (no gaps in the curve)
what are the born requirements used for
they’re used for eigen functions // values to see if they’re still good possibilities for being Y.
so what do the born requirements do
restricts things from being a possible solution for Y.
gives rise to quantisation of energy (not random)
‘a particle may possess only certain energies,, or it’s Y would be unacceptable’
- only certain particle energies can be Y solutions.
wait so what do the tables for eigen functions and values do
they define the operator T’
and see if certain functions could be possible Y solutions.
to be a Y solution it must be an eigen function,, eigen value,, and must satisfy the born requirements.
