the bohr model. do now (3/10/14) (pass in your hw): 1. what is an atom? 2. how would you describe...
TRANSCRIPT
The Bohr Model
Do Now (3/10/14) (pass in your HW):
1.What is an atom?2.How would you describe
the structure of an atom?3.Draw a picture of an atom
as you picture it. 4. Up until about 1900,
what were some models of the atom and who developed these?
The Bohr Model of the Atom
3/10/14
Progression of the Atom 1704 Newton Proposed a mechanical universe with small solid masses in motion. 1803 John Dalton an "atomic theory" with spherical solid atoms based upon
measurable properties of mass. 1832 Michael Faraday Studied the effect of electricity on solutions, coined term
"electrolysis" as a splitting of molecules with electricity. Faraday himself was not a proponent of atomism.
1869 Dmitri Mendeleev Arranged elements into 7 groups with similar properties. He discovered that the properties of elements "were periodic functions of the their atomic weights". (Periodic Law.)
1894 G.J. Stoney electricity made of discrete negative particles he called electrons ".
1900 Soddy Observed spontaneous disintegration of radioactive elements into variants he called "isotopes" or totally new elements
1903 Nagaoka Postulated a "Saturnian" model of the atom with flat rings of electrons revolving around a positively charged particle.
1904 JJ. Thompson Plum pudding model 1905 Albert Einstein Published the famous equation E=mc 2 1909 R.A. Millikan Oil drop experiment determined the charge (e=1.602 x 10 19 C)
and the mass (m = 9.11 x 10 -28 g) of an electron. 1911 Ernest Rutherford Using alpha particles as atomic bullets, probed the atoms
in a piece of thin (0.00006 cm) gold foil . The nucleus was: very dense, very small and positively charged. also assumed electrons were located outside the nucleus.
View of atomic Structure in early 1900’s
+Electronorbit
electrons traveled around the nucleus in orbits, like the planets
Classical (before 1900) physics could not explain why electrons don’t fall into the nucleus
The Bohr Model 1922 Niels Bohr Developed an explanation of
atomic structure that underlies regularities of the periodic table of elements. His atomic model had atoms built up of successive orbital shells of electrons.
Bohr’s Model
Nucleus
Electron
Orbit
Energy Levels
Nucleus
Electron
Orbit
Energy Levels
Bohr’s Theory
classical view is wrong developed a new theory (now called quantum mechanics)
Electrons only exist in certain orbits (called stationary states.)
electrons are restricted to QUANTIZED energy states.
Energy only comes in discrete chunks!
Further from the nucleus means more energy
There is no “in between” energy
First
Second
Third
Fourth
Fifth
Incr
easi
ng e
nerg
y }
n=quantum number
Only orbits where n =positive integer are permitted.
Energy of quantized state = - 13.6/n2
• Radius of allowed orbitals rn = n2 (0.0529 nm)
n = 1
n = 2E = -C (1/22)
E = -C (1/12)
Radius of electron orbits: Another way:
rn h2n2
4 2kmq2 (5.3x10 11m)n2
Energy of one electron: E:
The ionization energy is equal to the negative energy of the electron
En 13.6eV
n2
KE The kinetic energy of the electron
KE Eabsorbed E ionization 1
2mv 2
Example:
Calculate the radius of the orbital associated with the energy level E4 of the hydrogen atom.
Example:
Calculate the energy of the orbital associated with the energy level E3 of the hydrogen atom.
Calculate DE for electrons in Hydrogen “falling” from n = 2 to n = 1 (higher to lower energy)
n = 1
n = 2
En
erg
y
DE = Efinal - Einitial = -13.6 [(1/12) -
(1/2)2] = -(3/4)C
Practice:
Use the rest of class to work on the paper: “Intro to the Bohr Model.” It is due on Friday
n = 1
n = 2
En
erg
y• - sign for DE indicates emission •+ for absorption• since energy (λ, f) of light can only be + •it is best to consider such calculations as DE = Eupper - Elower
n = 1
n = 2
En
erg
y
The Bohr Model
The Bohr Model When an electron loses energy and drops to a lower state, a photon is released with energy:
Ephoton = hf =hc/λ = Ehigher state–Elower state
E of photon: Other ways:
2.17x10 18J
nhigherstate2
2.17x10 18J
nlowerstate2
13.6eV
nhigherstate2
13.6eV
nlowerstate2
The Bohr Model
The Ground State The lowest energy state
Example:
An electron drops from the 4th energy state to the 2nd. What is the energy of the photon emitted?
From Bohr model to Quantum mechanics
Bohr’s theory was a great accomplishment and radically changed our view of matter.
But problems existed with Bohr theory: theory only successful for the H atom. introduced quantum idea artificially.
So, we go on to QUANTUM or WAVE MECHANICS
Hydrogen-like Atoms (atoms that have been ionized so that they
have one electron left)
En mek
2Z 2e4
2h2n2
Z 2(13.6eV )
n2
Practice: Complete The Bohr Atom Classwork If you finish early, submit it and begin working
on your homework
n = 1
n = 2
En
erg
y
so, E of emitted light = (3/4)R = 2.47 x 1015 Hz
and l = c/n = 121.6 nm (in ULTRAVIOLET region)
C has been found from experiment. It is now called R, the Rydberg constant. R = 1312 kJ/mol or 3.29 x 1015 Hz
This is exactly in agreement with experiment!
Atomic Spectra and Bohr Model (7)
Hydrogen atom spectra
Visible lines in H atom
spectrum are called the
BALMER series.
High EShort lHigh n
Low ELong lLow n
En
erg
y
Ultra VioletLyman
InfraredPaschen
VisibleBalmer
En = -1312 n2
65
3
2
1
4
n
Atomic Structure Niels Bohr Bohr model of the atom Energy level diagrams
Bohr and Quantum Hypothesis Discharge spectra hf=Eu – Ei where Eu is energy of the upper
state. Orbit closest to the nucleus has lowest energy
(most negative). An electron at infinite distance has energy of 0 eV.
Do Now (3/11/14):An electron is in energy state #5.
1.What is the radius of the orbit?
2.What is the energy of the electron?
Energy Level Diagrams Minimum energy to remove an electron is
binding energy or ionization energy. 13.6eV – energy required to remove an
electron from the lowest state E1= -13.6eV up to E=0.
Lyman series, Balmer series, Paschen series for hydrogen atoms. – pg 848.
Characteristic X-rays
Buckyballs
Practice: Complete the Bohr Atom classwork Check your answers with the key at the front
of the room When you get 100%, submit your work and
begin to work on your homework
Do Now (3/12/14):
Do Now (3/11/14):
An electron is in energy state #5.
1.What is the radius of the orbit?
2.What is the energy of the electron?
Quantum quizzes!
Atomic Spectra
• Atoms in heated gases emit and absorb light of certain wavelengths.
• Shown above are three emission spectra and one absorption spectrum.
Why Do Excited Atoms Emit Light In Narrow Bands (lines)
Line Spectrum of Atomic Hydrogen
In 1885 Johann Balmer discovered an equation which describes the emission-absorption spectrum of atomic hydrogen:
1 / l = 1.097 x 107 (1 / 4 - 1 / n2)
where n = 3, 4, 5, 6, ...
Balmer found this by trial and error, and had no understanding of the physicsunderlying his equation.
Why are there lines in the first place?To answer this question we have to understand a few things
Neils Bohr Explains the Hydrogen Atom and Balmer’s Results
Neils Bohr, a Danish physicist, treated thehydrogen atom as if it were an electron ofcharge -e orbiting in a circular path abouta proton of charge +e.
Bohr Model
Review:
Energy Levels in Hydrogen
En = -13.6 eV /n2 ----------------------- E1 = - 13.6 eV E2 = - 3.40 eV E3 = - 1.51 eV E4 = - 0.85 eV E5 = - 0.54 eV E6 = - 0.38 eV
Energy Transitions in Atoms
Energy of photon = Energy lost by electron hf = Ei - Ef
Calculating Wavelengths of Emitted Light
hf = Ei - Ef E3 ---> E2:Ei = - 1.51 eVEf = - 3.40 eV------------------------------hf = - 1.51 - (-3.40) = 1.89 eV------------------------------l = (1240 eV-nm) / E
= 1240 / 1.89 = 656 nm
Review:
Wavelength corresponds to which characteristic of light???
Color!!!
Balmer and Rydberg
Rydberg constant:
1
RH
1
22 1
n2
The wavenumber
Balmer Series
Wavelength(nm)
Relative Intensity
Transition Color
383.5384 5 9 -> 2 Violet
388.9049 6 8 -> 2 Violet
397.0072 8 7 -> 2 Violet
410.174 15 6 -> 2 Violet
434.047 30 5 -> 2 Violet
486.133 80 4 -> 2 Bluegreen (cyan)
656.272 120 3 -> 2 Red
656.2852 180 3 -> 2 Red
Other Energy Transitions
The final state in the energy transitions is n = 3 for the Paschen series, n = 2 for the Balmer series, and n = 1 for the Lyman series.
Recalling that the range ofvisible wavelengths isapproximately 300-700 nm,one can see that only transitions ending at n = 2 emit light in the visible range
Atomic Challenge Work with your group to complete the Bohr
Atom Challenge The first group to get 100% gets a bonus!
The Bohr Atom: Complete the classwork Use the rest of class to work on your hw
Do Now: 3/12/14:
1. If hydrogen’s ground state energy were -8 eV, what would be the wavelength of the photon emitted when an electron drops from the first excited state to the ground state?
2. Does the Bohr model explain why only certain electron energy levels exist?
PASS IN YOUR CW FROM YESTERDAY
IF YOU HAVE NOT
ALREADY DONE SO!!!
Does the Bohr model explain why only certain electron energy levels exist?
He figured out the equation to predict the spacing between all of the energy levels of any one-electron atom or ion.
His model was quite successful, and he was able to predict which lines you would see for things that hadn't even been measured yet.
Surprisingly, although he figured out the pattern so well, he didn't actually know what the patterns were really due to. In fact, he had to make assumptions that turned out to be completely false!
Despite these errors (corrected when quantum mechanics was developed), the Bohr model of the atom is very useful for many applications.
His model does NOT work well for multi-electron atoms/ions, which, unfortunately, includes the large majority of atoms and ions! You need quantum mechanics for that!
Lab! No more than four people in a group One paper per group
Do Now (3/13/14): Write down today’s objective. Which model that you observed yesterday
was the most correct? Why? How could today’s objective relate to the
question above?
The correct model is….
Schrodinger!!!! Why??
Schrodinger Schrodinger predicts not only the presence of
energy levels and their values, but the PROABILITY that an electron is in any given state at any given time
What were the states of the cat???
Agenda (25 min)1. Find your group and an area of the room to
work.2. Complete your portion of the guided note
sheet (check with the key or me when you are finished)
3. Represent your portion of the notes in an info-graphic on the chart paper provided to you. Please include at least one picture or diagram. (bonuses will be awarded to those voted to be the most informative and best looking charts)
4. It may help to sketch your work out before putting it on the chart part
You have 5 min to: Finish your work Check over and ensure that ALL information is
on your chart Staple your portion of the notes to your chart Hang it in the designated area! (Check the
number on your group’s note sheet)
Time is up!!
Place your work in a designated area around the room and wait for further instructions.
Objective
How does today’s objective relate to this assignment?
Agenda pt. 2
With your group, move to the next station. You will have two minutes at each station to fill in
your guided note sheet and to evaluate the work of your peers according to the rubric
You will rotate to each group to complete your note sheet and the rubric
You will also evaluate your peers based on the following criteria: most informative and most aesthetically pleasing
5 min: Finish your evaluation (don’t forget to briefly
justify each) Clean up Submit your rubric Begin your exit question
Exit Question
Draw a picture or representation of the following: A hydrogen atom One of the following series: (Balmer, Paschen, or
Lyman) OR explain what one of them is The generic formula for the wavenumber of energy
transitions in the atom How did today’s objective relate to this
assignment?
Do Now (3/14/14): What did you like about yesterday’s activity? What would you improve? Would you be interested in doing a similar
activity during our review unit?
Drawing Energy Level Diagrams: http://
www.s-cool.co.uk/a-level/physics/wave-particle-duality-and-electron-energy-levels/revise-it/electron-energy-levels
http://physics.bu.edu/~duffy/semester2/c37_energylevels.html
By the end of class… Two AP problems (review on the board) Rubric (collected) Guided note sheet (not collected)