6.1/6.2 Nature of Light and the Photoelectric Effect Flashcards
Light has both a wave like nature and a particle like nature. It simultaneously displays wave like charcteristics and particle like charcteristics
* Wave like chacteristics = wave length / frequency
* Particle like charcteristics = energy of a photon
Light behaves like a wave
* it has a set wave length and frequency
Wave length = any 2 points that are a wave apart
* its just the length of a wave
* lamda
Frequency = how fast the given wave lengths pass through a given point in space
* (v)
* it has the unit of per second (hz) - just the # of wave lengths passing through a certain point in space per second. So if its 5 per second, we may say 5 Hz is the frequency
c = speed of the wave
* in light this is 3.0x10^8 m/s (this deviates from this number when passing through different mediums) <— however, were always going to use the speed of light in a vaccum
lamda* v = C
* C is always a constant - this means lamda and v are inversly releated (if one is bigger the other must be smaller)
E (photon) = hv
* The energy of a photon is proportional to its frequency (v) - if you double the frequency you double the energy (can derieve this from the equation above)
* h = planks constant = 6.626x10^-34 (probs dont need to memeorize this)
* E = energy of a photon
* big thing you should realize is that v and E are directly proportional. If you double the frequency you double the energy
We can substitute in v = c/lambda in the ephoton equation
* Ephoton = h* c / lamnda
So the rods and cones and your eyes can only detect a small amount of the actual light thats out there. Thats called visible light
Electromagnetic radiation:
* Gamma Rays
* X-rays
* Ultra Violet (UV)
* Visible - we detect this one
* Infrared (IR)
* Microwaves
* Radio waves
Should know the realtive positions of these
Name the order of light rays as the rise in E
Gamma Rays
X-rays
Ultra Violet
Visible
Infrared
Microwaves
Radiowaves
Light rays get more harmful to humans as they rise in energy
* So gamma rays would be the worst to come into contact w/ - these are found in nuclear radiation
So if energy is increasing, frequency must also be increasing because they’re directly porportional (E = hv)
* however, wavelength is inversly portional, meaning it goes the opposite way as the other 2
* Increased frequency means increased energy, however it means decrease wl
* increased energy = increased frequency but decreased wl
* increased wl = decreased frequency and energy
Meaning gamma rays have the greastest frequency and energy but the smallest wave length
Visble light E order
* Violet
* indigo
* blue
* green
* yellow
* organge
* Red
* Roy, G, Biv is out nmenumonic
name the order of visible light
Visble light E order
* Violet
* indigo
* blue
* green
* yellow
* organge
* Red
* Roy, G, Biv is out nmenumonic
red light wl
700nm
so if you’ve got a longer wl than this you’re at least in infrared light (because longer wave length = decrease E)
violet wl
400 nm
if you’ve got a shorter wl than this you’re at least in ultra violet light (because shorter wl = increased E)
Knowing any 1 of the 3 variables below will allow you to find the other 2 as long as you know all these equations. So only need 1/3 not 2/3
What is the frequency and energy of a photon w/ a wavelength of 400nm?
Need to get nm to meters because frequency is in 1/s (number of times it happens per second) so we need to get the meters to cancel out
E photon = 4.97x10^-19 J
* to power your house this like no energy at all. You would need trillions this. however, to an electron this is a lot of energy. Electrons will absorb energy
* We utilize a different unit rather than jouels for electrons, called electron volts
* 1 electron volt = 1.6x10^-19J
* So our answer below would be 3.1eV (electron volts) - this equation always gives us the energy of 1 electron, if they asked for a mol of photons you would multiply by 6.022x10^23
Photoelectric Effect
* Energy of a photon or electron can only have specific quantities
Say you had a quantum car, that would mean it could only go certain speeds
* first gear = 10 mph
* second = 20
* so basically those are the only speeds your car is allowed to do - you will never find your car doing other speeds
* so when you shift gears from first gear to second gear its not like it speeds up through the teens, it litteraly jumps from 10 to 20 without touching anything in the middle
So electrons have a certain amount of energy associated w/ them. And you can knock one of those electrons out of the metal showed below if you hit it w/ light. But that light has to have the correct amount of E. So the proton of light has different energies based on its frequencies or wave lengths (which again our eyes interpret as different colors)
* a bright light would have more photons and a faint one would have less, however the photons in that light are going to all have the same amount of E (if its all the same kind of light think gamma)
* if you have blue light over red light, that blue light is going to have more energy associated w/ it
Work function = the minimum amount of energy it would take for a photon to eject an electron from that specific metal
* these are different depending on the materal were working w/
* so in the picture below it says our work function = 2eV. Well if we started hitting that metal w/ photons of just 1 electron volt, no electrons are going to get ejected, because it would need to be at least 2eV
if the photons are at least 2eV in this case, they have the opportunity to eject ONE electron. Its a 1:1 ratio, a photon can’t eject more than 1 electron
* now amgine we changed it to violet light (which is 3eV), thats more than the work function, so electrons would start getting ejected.
Now the ejected electrons velocity will vary depending on the energy of the light that its hit w/. So if its hit w/ 2eV of energy its velocity when flying away will be lower than if its hit w/ 4eV from the photon.
So the equation below basically says any excess kinetic energy that that electron is hit w/ (the photon is more than 2eV in the example below) the electron gets to keep it as kinetic E as it moves away
gamma rays
ultra violet
meaning from least to most
meaning it happens 4x10^14 per second (thats what 1/s or s^-1 means)
hardest part was rmemebering to convert nm to get the meters part to cancel out
basically when a photon of 10eV hits a metal plate it took 3eV to detatch the electron, so it flew away at 7eV.
Bohr Model
He said at the center of the atom is a nucleus, and electrons go around this nucleus at set orbits. So by having set orbits around the nucleus they will have set energies
When you drop something it will lose potential energy (because it doesnt have as far to fall) and gain kinetic energy
* so any two objects will have some amount of gravitational PE. However, the closer they get together, the lower their potential energy becomes
* The same thing is true for the negatively charged electrons attracted to the postively charged nucleus. When its in that first orbit (first circle below), thats when it will have the least amount of PE (essentially doesnt have as far to fall toward the nucelus at this point). And the further it is out from the nucelus the more PE (were just gonna call it energy from now on) it will have
En = -2.18x10^-18 J / n^2
* this is the equation to predict the PE of an electron in any orbit
* n corresponds to the invidiual orbits. So the closest orbit below is n = 1
NOTE: the further you go out the closer these orbits get together
* and there is an infinite # of orbits
* it goes all the way up to infinity
* however in our equation above if we plug in infinity for n, we get 0 becuase anything dividied by infinity = 0
* so basically as you go up in orbit the electron really isnt even part of the atom anymore, so it has 0 potential energy at this point (because anything divided by infinity is 0)
The potnetial energy becomes less negative (gains potential energy) as the electron moves further from the nucelus, just like in gravity
If the electron falls back to a lower orbit (closer to the nucleus), it loses potential energy but gains kinetic energy, just like an object falling toward the earth
The reason the electron is at its lowest energy at n = 1:
* The attraction pulls the electron inward
* To keep it from crashing into the nucleus, it must be moving (has kinetic energy)
* The total energy of the system (kinetic + potential) is mist negative in the lowest orbit, meaning it’s the most stable
* In physics, the lower energy = more stable
* if the electron is in n = 1, you’d have to add the most energy to pull it away (ionize it)
* if its in n = 2, its already partway out the door - takes less E to free it
* so the electron naturally “falls” into the lowest possible orbit unless energy is pumped in to push it up think a photon
Shown below in red, electrons can jump to different orbits, however, its going to take energy to do that because its at its lowest energy in the first orbit, so to go outwards it will need more E.
* absorbing a photon will push it into the more peripheral orbits
* if its going to go from an n = 1 to an n = 2 orbit, its going to have to absorb exactly that much E
* and the orbits are all a certain length apart, meaning we know exactly how much E they need to jump to orbits (can’t land somewhere in between because they’re quantom) –> it only exists at specific quantities. Because of this, only certain photons could get absorbed
* going from n = 1 to n = 4 or n = 2 to n = 3 or any combo will correspond to a specific photon
Zero energy is defined as the state where the electron is completely free from that atom. It has escaped the nucleus entirely
Any state less than zero means the electron is bound to the nucleus and would need energy added to escape
So negative potential energy just means the electron is stuck in the atom, and it would take positive energy input (like absorbing a photon) to free it
The reason is gets less negative, or closer to 0 as you get into the outer rings means its less tightly bound - because its further from the nucleus, so it takes less E to remove it
Find the change in E between E1 and E3 (goes from E1 to E3)
= 1.938x10^-18
* so it needs energy to be moved to the outer orbits
* This makes sense, because its at its lowest energy (most stable) state in the lowest orbit, and E would need to be added to the electron to move it out of this state
* So if an electron is going to jump from that first orbit to that 3rd orbit, its going to need to absorb exactly that much E because its quantum
* so the photon its going to absorb needs to have exactly that much E
So that difference between E3 and E1 must = the energy of that photon
* E(photon) = 1.938x10^-18 J
shown the next slide is another way to calculate delta E using a formula w/o having the calculate the energy levels of N = 1 and N = 3
Remember this delta E is the amount of E needed to move electron from n = 1 to n = 3, but it also = the amount of energy the photon has as well (because it will need to have exactly that much E to move it to those peripheral orbits)
Energy of a photon can never be a negative number
* if you go from a centeral orbit to a more peripherla 1, than you need to absorb a photon
* if you go from a more peripheral orbit to a more central one, than you will need to emit a photon - when you calculate delta E for this you will get a negative number, this doesnt mean the photon was negative as well, it just means ones was emited - photons can never be negative #’s
* When you’re calculating photons E always take the absoulte value because theres no such thing as negative E for a photon
notice below we got the exact same number
* again, its this E that the electron absorbs to move from orbit 1 to orbit 3 and this = the E of the photon
* remember the Ephoton = hv or hc/lamda
* so in finding that delta E you can use it to find either the frequency or the wave length
So the below is showing how to actually calculate the wavelength in the photon itself from finding the delta E of the electron
White light = continuous spectrum of all the colors
* if you use a prism you can spread this out int all the colors
If you take that white light coming off the sun, there are going to be certain colors that are missing (shown below)
* the missing colors corespond to wavelengths that have been absorbed.
* the white light is created from the nuclear rxns in the core of the sun, then it has to pass through the outer peripheri of the sun, which contains a lot of hydrogen gas. That hydrogen gas is going to absorb very specific wave lengths (because remember, electrons can only absorb photons at very specific wave lengths get them to deviating orbits, because those electrons are quantum and can only absorb specific #’s)
* this is how we know the sun is made up of primarily hydrogen
* so we know what the suns made out of because we can see what colors are missing
* we can also figure out what other stars are composed of based off the light coming off of them
This is the emission spectra. remember, the orbits get closer as you get further away from the nucleus
So this is another way to look at the bhor model
Energy goes up as you get further out (again, this makes sense because when you absorb a photon you’re brough to further away orbits)
The energy needed to jump orbits gets smaller the more peripherla you go (because those orbits are closer together)
* the most E we would need to jump orbits is between N = 1 and N = 2
If you take a sample of gas and zap it w/ electricity, you need up causing all the lower lvl electrons to jump up to higher n values. and then they’ll fall back down, and as they’re falling back down they will emit photons of light
* we don’t have light at all until we see those emitted photons
These photons might fall all the way back down to N = 1.
* some might have gotten zapped up to 2 others 3 etc…
* however some might only fall to 2
* when they all fall to the same orbit, they’re called a series
The difference in E for the black series below is bigger than the red series (meaning F - I is a bigger #)
Balmer series = when they drop down to n = 2
* A lot of the ones in this series corresponds to visible light
* Just know this 1 because its visible light we can see w/ our eyes
Limer series = when they drop down to n = 1
* These are bigger E photons and typically correspond to the ultra violet region
* notice the F - I E amount is much higher here, meaning its more than visible light would be
Passen series
* when they drop down to n = 3
* these are smaller E differences than the balmer series, and if the balamer was visible, than these must not be, these are more likely the infrared range
Bracket series
* When they drop to n = 4 (not shown below)
remember, they arent all the same distance apart. N = 1 to get to N = 2 takes more E than N = 2 –> N =3 would
Remember, frequency and energy are directly porportional. So it would be the ones that need to biggest E to get to
* Its wavelength thats inversely proportional
n = 2 –> n = 5
This one is hard. Def look back over it. The text at the bottom is what made it make sense to me.
This ones more tricky because its like a double negative
emession = were emitting a photon (letting it go). This happens when were moving to lower E levels
however, were talking about wave length
* bigger wave length = lower E
n = 2 –> n = 1
* a photon is emitted when an electron drops down from a higher shell # to a lower 1
If i want the longest wave length, i actually want the lowest energy photon and the smallest gap
2 – > 1 is the smallest gap
* it would be the lowest E photon, and lower E = bigger wave length
