Chem I Lesson 2: Photoelectric Effect, Absorption/Emission of Light, Bohr Model/Line Spectra
Find the wavelength of light that corresponds to an electron moving from n=3 to n=2
*i = lower energy level *j = higher energy level 1/λ = R[(1/i²)-(1/j²) 1/λ = (-1.097 x 10^7)(1/4-1/9) λ = 656nm = 6.56 x 10^-9
What is the magnitude of energy needed to take an e- away from the Hydrogen atom, aka to IONIZE the H atom?
+13.6 eV This accurately corresponds to Hydrogen's ionization energy. Bohr correctly predicts ionization energy for Hydrogen The point where e- is infinitely distanced from the Hydrogen atom is r = ∞. At r = ∞, it feels no attractive pull from the H nucleus, therefore there is no potential energy. So r = ∞ and E(total) = 0 because UE and KE both = 0. This is when the e- is IONIZED and Hydrogen atom goes from neutral to the cation H+.
What is energy of Hydrogen electron in radius 1 in electron volts?
-2.17 x10^-18 J = 1eV/1.6 x 10^-19 J = -13.6eV
How much energy would a Hydrogen electron need to gain in order to jump from n=1 to n=2? from n=1 to n=3?
-3.4-(-13.6) = 10.2 eV -1.51-(-13.6) = 12.09 eV
What are the 4 main types of radiation
1. Electromagnetic Radiation 2. Particle Radiation 3. Acoustic Radiation 4. Gravitational Radiation
Why is the Bohr model so useful in describing the structure of the atom?
1. Says that energy is quantized 2. Explains the formation of discrete line spectra produced by individual atoms
pico (p)
10^-12 (0.000000000001)
micro (μ)
10^-6 (0.000001)
nano (n)
10^-9 (0.000000001)
1 nm = ? m
10^-9 m
hecto (h)
10^2 (100)
mega (M)
10^6 (1,000,000)
What is the value of the Rydberg constant in Joules?
2.178×10−18 Joules/electron
What range is the visible light spectrum?
700-400 nm red - ultraviolet
What is flourescence?
A phenomena related to absorption/emission of visible light. If a fluorescent substance is excited with UV radiation, it will begin to glow with visible light. 1. UV radiation excites electron in fluorescent substance to a higher energy state 2. Electron returns to its original state in two or more steps *Multi-step down is characteristic of flourescence - Each step involves less energy. At each step: a photon is emitted with a lower frequency/longer wavelength than the absorbed UV photon - If the wavelength of this emitted photon is within the visible range, it will be a seen as light of the particular color corresponding to the wavelength
How does the mass spectrometer separate components based on their mass if the equation F = qvB doesn't include mass?
All components have the same velocity and the same +1 charge going into a mass spectrometer. They all experience the same magnetic force from the magnetic field. Mass is determined by the RADIUS in which the component's arc takes.
What are the 3 main types of particle radiation?
Alpha radiation / Beta Radiation / Neutron Radiation
What does an absorption spectrum measure?
An absorption spectrum measures the radiation absorbed when electrons absorb energy to move to a higher energy state.
What does "absorption" refer to in regards to electrons in energy levels of orbitals?
An electron can jump from a lower energy level to a higher energy level by ABSORBING a photon of light of precisely the right frequency to match the energy difference between orbitals (E = hf). If the photon doesn't have enough energy, the electron can't make the jump to a higher energy level
Electromagnetic wave
As a charge vibrates, it accelerates and produces a changing electric field. This movement of charge creates a changing magnetic field that can in turn induce a changing electric field. The two fields are perpendicular. As electrical and magnetic fields regenerate one another, an ELECTROMAGNETIC WAVE, a traveling oscillation of an electric and magnetic field, emanates from the vibrating charge
What equation derived from the Bohr model can be used to relate different wavelengths to different energy levels in the atomic emission spectrum?
Balmer Rydberg Equation n2 is the higher energy level/n1 is the lower energy level ** Rydberg constant is actually 1.097 x 10^7 1/m
Which emission line series is in the visible light spectrum?
Balmer Series 656nm-410nm
Why do we only talk about electrons (and not protons or neutrons) being ejected from metals?
Because of the weak hold that metals have on their valence electrons due to their low ionization energies.
Why can gamma rays actually damage DNA?
Because they have the shortest wavelengths/highest frequencies and can penetrate more so than other electromagnetic waves
What are the biggest and smallest "pieces" that come out of a mass spectrometer?
Biggest: The entire original molecule except for one electron Smallest: a single proton, H+
What effects the speed of ejected electrons?
Color of the light (not intensity or brightness!). Blue light results in much speedier electrons than red light.
Relate Coulomb's law and force equation to angular momentum to find the radii and velocity of orbitals and electrons, respectively.
Coulomb's law and force equation: Fe = K⋅q₁⋅q₂/r² = m⋅ac Fe = Ke²/r = mv²
How is current related to the intensity of light beam in the photoelectric effect?
Current is directly proportional to the intensity of the light beam, as long as light's frequency is above threshold frequency.
What equation relates energy of a photon to its frequency?
E = hf E = Energy of a photon of light or quantum h = Planck's Constant (6.626 ⋅ 10^-34 J⋅s) f = Frequency of light wave/radiation (Hz) *symbol for frequency is also ν ** E = hf is the amount of energy carried by light. It is dependent on frequency, not intensity of light.
Give equation for Energy of electron at radius n
E(n) = -1/2(Ke²/r(n)) *r(n) = radius n (could be 1,2,3...) OR E(n) = E(1)/n² = -2.17 x10^-18 J/n²
What is energy of Hydrogen electron in radius 2 in electron volts?
E(n) = E(1)/r(n)² E(2) = -13.6eV/4 = -3.4eV
What is energy of Hydrogen electron in radius 3 in electron volts?
E(n) = E(1)/r(n)² E(3) = -13.6eV/9 = -1.51eV
What is the energy of a Hydrogen electron radius 1?
E(total) = -1/2(Ke²/r) (E1) = -1/2(9.00 x 10^9N⋅m²/C²)(1.6x10^-19C)² / 5.3 x 10^-11 m *(1.6x10^-19C)² = charge of e- E1 = -2.17 x 10^-18 J *This is the energy of an e- at n = 1
Give equation for total energy associated with an electron
E(total) = UE + KE UE = potential energy (electrical potential energy in this case) KE = kinetic energy UE = K⋅q₁⋅q₂/r = K(e)(e-)/r = -Ke²/r *Note: this is not Coulomb's law although it is close. R is not squared in the denominator. *K = Coulomb's constant 9.00 x 10^9 N⋅m²/C² here as well though UE = = -Ke²/r *UE is negative! KE = 1/2mv² = 1/2Ke²/r E(total) = UE + KE E(total) = 1/2mv²-Ke²/r = 1/2Ke²/r - Ke²/r *See what we did here using the other definition of KE! E(total) = -1/2(Ke²/r)
Each element has a unique "fingerprint" called an ____________________. Why is it a "fingerprint"?
Each element has a unique "fingerprint" called an ATOMIC EMISSION SPECTRUM Because each element can have its electrons excited to a different set of distinct energy levels
What does the photoelectric effect's "all or nothing" characteristic have to do with the nature the light beam?
Einstein's explanation of the "all or nothing" phenomena of the photoelectric effect is that the light beam consists of light QUANTA, called photons, and that energy must be emitted/received in discrete packets (quanta) rather than on a continuous scale. The discrete-ness of light quanta is related to a threshold frequency (Tf) first needing to be met before electrons can be liberated
Coulomb's Law
Electric force between charged objects depends on the distance between the objects and the magnitude of the charges. Fe=Ke q₁*q₂/r², magnitude of force between two charges Fe = electric force Ke = Coulomb's constant = 9.00 x 10^9 N⋅m²/C² q₁ = charge on object 1 (ex: proton) q₂ = charge on object 2 (ex: electron) r = distance between the objects (In atom, this is the radius of the orbital with the electron of interest)
What is electromagnetic radiation?
Electromagnetic radiation is the emission/transmission of energy in the form of waves or particles through space or a material medium.
Electrons that are liberated from the metal by the photoelectric effect will produce a _________________
Electrons that are liberated from the metal by the photoelectric effect will produce a CURRENT: a net charge flow/unit time
What is the photoelectric effect?
Emission of electron when light of a sufficiently high frequency/shorter wavelength (blue --> UV) shines (is 'incident' on) a metal in a vacuum (or an atom's orbital ). The metal (or atom's orbital) emits electron(s) A photon hits an electron and knocks it loose - a "collision of two particles"
What is the equation for magnetic force in terms of magnetic field strength and velocity of an ion?
F = qvBsinθ F = Force q = charge of cation v = velocity B = magnetic field θ = angle between velocity and magnetic field = 90° so sin(90°) = 1 F = qvB(1) F = qvB
True or False: The parent peak is always the base peak
False, the parent peak could be the base peak but it's not always the case.
True or False: Intensity/brightness of light effects an electron's speed.
False. COLOR of light effects an electron's speed. Remember - greater intensity/brightness just means more photons are having one on one collisions with electrons. It doesn't say anything about the frequency/wavelength of that light. Only color of light described the frequency/wavelength. Short wavelengths have higher frequencies = more energy = speedier electrons
True or False: Energy of a photon increases with longer wavelengths
False. Energy of a photon increases with SHORTER wavelengths (that have higher frequency than longer wavelengths)
What does the first peak on a mass spectrometer represent?
First peak (all the way to left near y axis) represents the H+ cation where m/z or m/q (mass to charge ration) = 1
_________ intensity with which ion collides with magnetic field = __________________ abundance
GREATER intensity with which ion collides with magnetic field = GREATER abundance
Lymann Series
Group of hydrogen emission lines corresponding to transitions from n ≥ 2 to n =1 includes larger energy transitions than the Balmer series; has shorter wavelengths in the UV region of the electromagnetic spectrum. 122-94nm
Balmer series
Group of hydrogen emission lines corresponding to transitions from n ≥ 3 to n = 2 Wavelengths are in the VISIBLE LIGHT region of the electromagnetic spectrum. 656nm (reds) - 410nm (violets)
HIGHER mass = ____________ radius / ____________ semi circle arc SMALLER mass = ___________ radius / _____________ semi circle arc
HIGHER mass = LARGER radius / BIGGER semi circle arc SMALLER mass = SMALLER radius / SMALLER semi circle arc *Components that are more massive won't accelerate as much (F = ma: ↑m↓a) and will end up having an arc trajectory that is wider and has a greater radius.
In relating angular momentum and linear momentum to get L = rmvsinθ, why is the angle 90° making sin(90) = 1?
Here we are talking about the momentum about the center of our circle angle between two vectors: r and v (v is the momentum vector).
How do you convert joules to electron volts?
IeV = 1.6 x 10^-19 J
What is the difference between Infrared (IR) Spectroscopy and UV-Vis Spectroscopy?
Infrared (IR) Spectroscopy is used to determine chemical structure, since different bonds will absorb different wavelengths of light. UV Vis Spectroscopy goes one step further and looks at absorption of light in visible and UV range.
What is so significant of Bohr quantizing angular momentum?
It allowed for limiting the different kind of radii possible. Because of this, only certain radii are allowed and you can't find an electron that is in between r1, r2, r3 etc... r1 = 5.3 x 10^-11m rn = n²r1 *rn = radii of n level What's important about radii is that these orbitals are associated with different ENERGIES
What does an observed spectral line mean?
It means an electron has fallen down to a ground state from a higher level, releasing a photon. Each energy level corresponds to a discrete quantity of energy (-13.6eV, -3.4eV, -1.5eV) and when an electrons move down energy levels, they release photons with wavelengths corresponding to the transition.
Which equations could you use to technically find the velocity of an ejected electron?
KE = 1/2mv² KEmax = hf - w = h(f-Tf) 1/2mv² = h(f-Tf)
Relate kinetic energy equation to Coulomb's law and force equation to find energy of different orbitals Physics + General Chemistry
Kinetic Energy: KE = 1/2mv² *Here, we are taking about the KE of an electron. m is the mass of e- and v is the velocity of e- Coulomb's law related to force equation: Fe = Ke²/r = mv² *The trick here is to multiply both sides by "1/2" to recreate the KE equation!! 1/2Ke²/r = 1/2mv² tadaa!
Give formula for maximum amount of kinetic energy of an ejected electron
Kmax = hf - w Kmax = max kinetic energy (J?) h = Planck's constant (6.626 x 10^-34 J⋅s) f = frequency (Hz) w = work function of the metal/substance in question *Kmax essentially = energy of photon - work function of metal
Combine equation for Kmax in terms of work function
Kmax = hf - w w = h ⋅ Tf Kmax = hf - (h ⋅ Tf) Kmax = h(f - Tf)
What equation did Neil Bohr come up with for angular momentum that he thought should be quantized?
L = rmv = nh/2π n = some integer (think energy level!) h = Planck's constant = (6.626 ⋅ 10^-34 J⋅s)
Physics equation for angular momentum
L = r⋅p L = angular momentum (don't think this is "linear") r = a vector p = linear momentum
Light beams of greater intensity produce ______________ currents as long as the light beam's frequency is above the _______________________________ of the metal/orbital
Light beams of greater intensity produce LARGER currents as long as the light beam's frequency is above the THRESHOLD FREQUENCY of the metal/orbital
When does light become visible?
Light becomes visible when electromagnetic waves
Which emission line series has the largest energy transitions and shortest wavelengths?
Lyman Series - UV Light region 122-94nm
What is the work function?
Minimum energy required to eject electron. Related to Tf (threshold frequency) by: w = h ⋅ Tf w = work function h = Planck's constant (6.626 x 10^-34 J⋅s) Tf = threshold frequency
How can we relate Neil Bohr's equation for angular momentum to Coulomb's law/Force equation expression to find the radius of the first orbital in the Hydrogen atom?
Neil Bohr's equation for angular momentum: L = rmv = nh/2π v = nh/2πmr Coulomb's law and force equation: Fe = K⋅q₁⋅q₂/r² = m⋅ac Fe = Ke²/r = mv² *Plug in for v Ke²/r = mv² = m(nh/2πmr)² Ke²/r = m(n²h²/4π²m²r²) Ke² = (n²h²/4π²mr) r = n²h²/Ke²4π²m
Are photons deflected by a magnetic field?Why or why not?
No because only charged particles can be deflected by a magnetic field and photons are not charged
What and where is the parent peak in a mass spectrometer ?
Parent peak represents the cation of the original compound (parent ion) - the biggest "piece" that has everything intact except an electron. Parent peak is always farthest to the right on the mass spectrometer analysis
Which emission line series is in the Infrared light spectrum?
Pashchen Series 1875nm - 1094nm
What are the 7 different types of electromagnetic radiation (In order of decreasing wavelength)
Radiowaves / Microwaves / Infrared / Visible Light / Ultraviolet / X-Rays / Gamma Radiation
What is neutron radiation?
Results from nuclear fission/fusion. Consists of release of free neutrons from atoms which react with nuclei of other atoms to form new isotopes (which can in turn produce radiation)
What is spectroscopy, generally?
Spectroscopy is the study of the interaction between matter and electromagnetic radiation.
If a photon of wavelength 525nm hits metallic cesium (work function = 3.43 x 10^-19 J), what is the velocity of the photoelectron that is produced
Step 1: Find energy of photon E = hf = h(c/λ) = (6.626 x 10^-34 J)[(3 x 10^8 m/s)/(5.25 x 10^-7 m) ESTIMATE: E ≈ (7 x 10^-34)(3 x 10^8) / 5 x 10^ -7) ESTIMATE: E ≈ 21 x 10^-26 / 5 x 10^ -7) E ≈ 4 x 10^-19 J actual Ephoton = 3.78 x 10^-19 J Step 2: Find KE KE = hf - w KE = Ephoton - w = 3.78 x 10^-19 J - 3.43 x 10^-19 J = 0.35 x 10^-19 J = 3.5 x 10^-20 J Step 3: Find velocity KE = 1/2mv² = 3.5 x 10^-20 J = 1/2(9.11 x 10^-31)v² v² = 7.0 x 10^-20 J / 9.11 x 10^-31 v² ≈ 0.8 x 10^11 ≈ 8.0 x 10^10 v ≈ 2.8 x 10^5 m/s
A particle is travelling through a mass spectrometer in a region of space where the electric field is 1500volts/meter and the magnetic field is 0.034 Tesla. The magnetic/electric forces balance one another so cation follows a straight path. Particle's radius becomes 0.027m. What is the mass of cation. (q = + 1.6 x10^-19 C)
Step 1: Find velocity of cation v = E / B = 1500 / 0.034 = 4.4 x 10^4 m/s Step 2: Calculate mass m = qrB/v m = (1.6 x10^-19) (2.7 x 10^-2)(3.4 x 10^-2) / (4.4 x 10^4) m ≈ (1.5 x 10^-19)(3 x 10^-2)(3x10^-2) / (4.4 x 10^4) m ≈ (13.5 x 10^-23) / (4.4 x 10^4) ESTIMATE m ≈ 3.5 x 10^-27kg ESTIMATE actual m = 3.3 x 10^-27 kg
What electrical phenomenon results from the application of the photoelectric effect?
The CURRENT created by the accumulation of moving electrons. Electrons "liberated" by photons will produce a current: a net charge flow/unit time.
What is the base peak in a mass spectrometer and what is it's relative abundance / relative intensity
The base peak is always the highest peak on a mass spectrometer and it has a relative abundance / relative intensity of 100 --> this means that it is the most recorded fragment/compound on the detector
What determines the absorption spectrum of a single atom?
The energy differences between ground-state electrons and high level electron orbits determine the frequencies of light - aka it's absorption spectrum - a particular material absorbs
What happens to the excess energy from the frequency of a photo that is greater than the Tf?
The excess energy from the photon with frequency > Tf will be converted to KINETIC ENERGY in the ejected electron
What is the photoelectron?
The freed electron that a photon releases. One photon creates one photoelectron
What does it mean for a light beam to have "greater /higher intensity"?
The higher/greater the intensity of a light beam, the greater the number of photos per unit of time that fall on an electron in an atom This produces a greater number of electrons per unit of time that get "liberated" from an electron shell in an atom --> larger current
The lifetime of an excited state electron is ________, so an electron will return rapidly to the ________________________. When an electron returns to the ground state, each will emit a photon with a __________________ characteristic of the specific energy transition it undergoes. The spectrum is composed of light at specific _________________.
The lifetime of an excited state electron is BRIEF, so an electron will return rapidly to the GROUND STATE. When an electron returns to the ground state, each will emit a photon with a WAVELENGTH characteristic of the specific energy transition it undergoes. The spectrum is composed of light at specific FREQUENCIES.
Which peak could be even farther right than the parent peak in a mass spectrometer and why?
The p+1 peak might be even farther to the right because this accounts for heavier isotopes than *elsewhere in notes this is called pH peak?
Which physics law can Coulomb's Law be related to in order to find the RADII and VELOCITY of orbitals and electrons, respectively
The physics equation for Force, (F = ma) can be related to Coulomb's law to find the radii and velocity of orbitals and electrons, respectively. Fe = K⋅q₁⋅q₂/r² = m⋅ac ac = centripetal acceleration = v² / r Fe = K⋅q₁⋅q₂/r² = m⋅(v²/r) Fe = K⋅(e)(e-)/r² = m⋅(v²/r) --> (e)(e-) means charge of proton and charge of electron. We take the absolute values of these because we're only interested in the magnitude of the charge. This expression then just becomes e². Fe = K⋅e²/r² = m⋅(v²/r) = K⋅e²⋅r/r² = mv² Fe = Ke²/r = mv² Ke²/r = mv² *Connecting general chemistry and physics!
What does the threshold frequency (Tf) overcome?
The pull that the protons in the nucleus have over electrons. (Coulomb's Law)
What is light, exactly?
The transfer of energy through alternating electric and magnetic fields. Does not require a medium.
What is the wide range of colors in fluorescent light the result of?
The wide range of colors in fluorescent lights is the result of the distinct MULTI STEP emission spectra of different fluorescent materials.
How does a mass spectrometer work?
This machine shoots a concentrated electron beam through a chemical or organic compound. The beam breaks bonds and produces different "pieces" all with a +1 charge. The beam creates different cation fragments that can then be analyzed based on mass to charge ratio.
True or False: Actual Kmax could be anywhere between 0 and Kmax
True
True or False: Balmer Rydberg Equation explains the emission spectrum of Hydrogen
True
True or False: Because each piece/component that results from a mass spectrometer's electron beam is a cation, they all behave in the same way in an electrical system
True
True or False: Changes in molecular structure can cause dramatic shifts in the absorption patterns of a substance
True
True or False: Knocking electrons loose causes a current of electrons to flow
True
True or False: An emission line spectrum is characteristic of a given element.
True. When excited electrons fall from a higher energy state to a lower energy state, energy is released. This energy creates an emission line spectrum that is characteristic of a given element.
True or False: Light acts as a particle and a wave.
True. The photoelectric effect is strong support for this. Light is not a continuous wave but acts like discrete bundles of energy called photons
Waves with _____ frequency have shorter wavelengths and ________________ Which wavelengths are these?
Waves with HIGHER frequency have shorter wavelengths and HIGHER ENERGY Shorter wavelengths are towards the blue and UV end of the spectrum (400nm ---> 1nm range)
Waves with _____ frequency have longer wavelengths and ________________ Which wavelengths are these?
Waves with LOWER frequency have longer wavelengths and LOWER ENERGY. Longer wavelengths are towards red and infrared end of the spectrum (1mm <---- 700nm range)
What does "emission" refer to in regards to electrons in energy levels of orbitals?
When an electron falls from a higher energy level down to a lower energy level, a photon of light is emitted with an energy equal to the energy difference between the two orbitals *In Orgo, it gets more complicated than just one electron (Ch. 11-Spectroscopy)
What is emission?
When an electron falls from a higher energy level to a lower energy level, it emits light in the form of a photon.
What are the x and y axis of a mass spectrometer?
Y-axis: relative abundance/relative intensity X-axis: mass to charge ration (m/q or m/z)
line spectrum
a spectrum that contains radiation at only certain specific wavelengths - in this case, the wavelength that corresponds to a specific electron transition.
mass spectrometry
an analytical technique that ionizes chemical and organic species and sorts the ions based on their mass-to-charge ratio. Mass spectrometry is used in organic chemistry to find the mass of organic compounds but is based in the principles of physics. Key to mass spectrometry are the properties of electrons and the force formulas in physics.
Waves
any disturbance that transmits energy through matter or space.
How do you find wavelength from frequency? (And vice versa)
c = fλ = νλ c = speed of light (3.00 x 10^8 m/s) f/ν = frequency of light (Hz) λ = wavelength (m)
10^-2 (0.01)
centi (c)
What is ionization energy?
energy required to remove an electron the minimum energy required to move an electron infinitely from the ground state of an atom
What are all the peaks collectively called on a mass spectrometer
fragmentation pattern
10^9 (1,000,000,000)
giga (G)
Paschen series
group of hydrogen emission lines corresponding to transitions from energy levels n ≥4 to n=3 Wavelengths are in the INFRARED LIGHT region (left of red = bigger wavelength) 1875-1094nm
10^3 (1000)
kilo (K)
10^-3 (0.001)
milli (m)
Physics equation for linear momentum
p=mv *Think about this equation in terms of the general chemistry. Here, we're talking about linear momentum of electron!
What is the equation for the radius of a cation's path (aka position on the detector) in a mass spectrometer?
r = mv/qB m = mass v = velocity q = charge of cation B = magnetic field
What is the radius of Hydrogen's first orbital?
r = n²h²/Ke²4π²m r = (1²)(6.626 ⋅ 10^-34 J⋅s)² / (9.00 x 10^9 N⋅m²/C²)²⋅4π²⋅(9.11x10^-31kg) *m = (9.11x10^-31kg) = mass of electron r1 = 5.3 x 10^-11m
What is Hydrogen's radi level 2 in meters?
r2 = 2.12 x 10^10 m
What is Hydrogen's radi level 3 in meters?
r3 = 4.77 x10^10 m
Light
the transfer of energy through alternating electric and magnetic fields. Does not require a medium. Light is a wave and a particle
