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physical - yr2, s1 > 1b + 2b > Flashcards

1b + 2b Flashcards

1
Q

F = ma meaning equation

A

net force = mass x acceleration

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2
Q

when we hit a ball we know the balls

A

momentum and position in the air

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3
Q

if we know amts position and momentum we can say we know its

A

trajectory!!

the lines that guess where an object is gonna fall!!

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4
Q

H Y = EY is the

A

schrodinger wave equation!!

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5
Q

bc an e- is so small, what does it not have and what does it have

A

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

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6
Q

increase in frequency means what in terms of energy

A

an increase in energy

theyre proportional!!

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7
Q

E=hvn meaning

A

energy of ‘n’ photons

h = planks constant
v = frequency

normally E=hv only gives the energy of 1 photon of light.

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8
Q

brighter light means whattt,, in terms of photons and energy

A

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.

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9
Q

what does E=hv mean

A

it means energy is quantised

meaning its not random

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10
Q

how do we know energy in an atom is also quantised?

A

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.

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11
Q

rhydberg equation shows how energy levels are quantised,, what the equation

A

v = Rh (1/n.small.2 - 1/n.big.2)

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12
Q

what did bohr suggest

A

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

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13
Q

what did bohr suggest about energy

A

that energy is proportional to 1/n2

where n is the principle quantum number

bigger n = further from nucleus.

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14
Q

what is the bohr model limited to

A

it’s limited to H only

bc other atoms have multiple electrons which alter the amount of Z felt by the outer electrons

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15
Q

electrons have

A

wave particle duality

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16
Q

what did de broglie say

A

he said that all particles have a wavelength !!

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17
Q

wavelength = in terms of debrogles

A

h/mv

planks / mass x velocity. !!!

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18
Q

classical and quantum evidence for e- having wave particle duality

A

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.

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19
Q

the fact that when shot at Ni ,, e- bounced off like a wave,, tells us what

A

that they have wave particle duality.
that they can be diffracted,, like a wave.

like light forming a rainbow 🌈! and light is a wave.

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20
Q

taking the e- bouncing off the Ni as a wave,, what can we plot

A

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

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21
Q

units for the wavelength = planks / mv

A

planks = js
mass = kg
v = m/s

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22
Q

wavelength of a 1 kg brick going 10m/s
wavelength of an e- going 10^4 m/s

A

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

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23
Q

why do larger objects have a small wavelength

A

bc there’s a large difference between planks and it’s mass

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24
Q

why do smaller objects have a greater wavelength

A

bc their mass and planks constant are similar

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25
Q

describe the graph for the wave function against r + what this graph shows

A

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.

26
Q

how do we find wavefunction

A

we find the wavefunction by solving the schrödinger equation!!!!

HY=EY!!!!

27
Q

what does Y tell us (wave-function)

A

tells us the probability of finding an e- in an atom (at a certain distance)

28
Q

bc an e- is a quantum object,; what don’t we know

A

bc e- is a quantum object,, we dk it’s position or momentum!!!

larger wavelength as h and its mass is similar

29
Q

change in position and change in momentum (p and q) should beeeee

A

equal or larger than (h.dash//h)

(h.dash = h/2n) where n = pi.

we go over this iabbbb!!!

30
Q

if change in q aka change in position iss a really large number,, what does this mean

A

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.

31
Q

what is a large position uncertainty normally due

A

it’s normally due to the massss

large mass = classical object

= small wavelength = large position uncertainty

32
Q

H’ Y = EY is the + what are the different things

A

time independent schrödinger equation
H’ = hamiltonian operator.
Y = wavefunction.
E = energy of particles.

it relates wavefunction to the energies of the particles

33
Q

H’ is the ,,, which meanssss

A

hamiltonian operator

operator means we want to separate the 1st derivative !! and low-key find the second one aswell.

34
Q

how do we know if something is an eigen function

A

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

35
Q

if the 1st derivative of e^kx is Ke^kx,, what is the eigen value

A

the eigen value is the number in front of the eigen function

aka it would be ‘K’ this time.

36
Q

when ur done with checking if the 1st derivative is a eigen function and has an eigen value,, what else do u do

A

u do the same thing for the 2nd derivative

37
Q

when something has an eigen value,, what else is the next requirement

A

has to fulfill the born requirements

38
Q

born requirements

A

needs to be
normalised
finite
single valued
continuous

39
Q

what does H’ do

A

the hamiltonian constant describes the energy of the particles + includes all the terms that contribute TO the particles energy

( potential and kinetic)

40
Q

H’ is equal to

A

T’ + V’

kinetic energy + potential energy

bc it describes the energy of the particle including all the things that contribute to its energy

41
Q

KE

A

= 1/2mv^2

42
Q

p (momentum) =

A

mass x velocity

43
Q

KE = in terms of momentum (p)

A

KE = p^2 /2m

which is approx involved with T’ (kinetic energy)

44
Q

So what does T’ (kinetic energy) equal to =

A

T’ = (-h.dash^2 /2m ) (second derivative)

h.dash = h/2n
n= pi.

45
Q

If H’ is the energy of the particle and so equals T’ + V’ ,, how else can we write the schrödinger equation

A

(T’ + V’)Y = EY

which hopefully gives us an eigen value

46
Q

and if H’ = T’ + V’

and T’ = (-h.dash/2m)(second derivative) ,, how else can we write the schrödinger equation

A

[(-h.dash/2m)(second derivative) V’]Y = EY

this is for 1 particle,, of mass(m),, moving in one direction

47
Q

if V’ (potential energy) is 0 due to the particle being a free particle

what does H’ equal

A

H’ = T’

meaning the energy of particle depends on its kinetic energy aka how much it moves.

48
Q

if V’ is 0,, for a free particle,, how else can we write the schrödinger equation

A

T’ Y = EY

49
Q

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??

A

nope!!!

the value of ‘a’ will not alter it it’s an eigen function or not!!

50
Q

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??

A

nope!!!

the value of ‘a’ will not alter it it’s an eigen function or not!!

51
Q

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

A

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

52
Q

in the sin wave there are regions of

A

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!!

53
Q

what do we do to find the probability of finding a particle between x and dx

A

Y^2 dx = Y

54
Q

what’s the problem with plotting Y against r aka wavefunction against r

A

u can get a negative probability,, aka a negative wavefunction at a certain distance

55
Q

what do we plot instead of Y against r

A

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

56
Q

what is integration

A

area under a curve.

is equal to 1.

aka the probability of finding an e- here is 1!!

57
Q

born requirements for graph of Y^2

A

normalised ( integration =1)
finite (keeps going forever)
single valued ( nice curve shape)
continuous (no gaps in the curve)

58
Q

what are the born requirements used for

A

they’re used for eigen functions // values to see if they’re still good possibilities for being Y.

59
Q

so what do the born requirements do

A

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.
60
Q

wait so what do the tables for eigen functions and values do

A

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.

physical - yr2, s1 (12 decks)

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