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.John Dalton  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.Michael Faraday  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.)Dmitri Mendeleev  1894 G.J. Stoney electricity made of discrete negative particles he called electrons ".G.J. Stoney electrons  1900 Soddy Observed spontaneous disintegration of radioactive elements into variants he called "isotopes" or totally new elements 1900 Soddy  1903 Nagaoka Postulated a "Saturnian" model of the atom with flat rings of electrons revolving around a positively charged particle.Nagaoka  1904 JJ. Thompson Plum pudding model  1905 Albert Einstein Published the famous equation E=mc 2Albert Einstein E=mc 2  1909 R.A. Millikan Oil drop experiment determined the charge (e=1.602 x C) and the mass (m = 9.11 x g) of an electron. R.A. Millikan  1911 Ernest Rutherford Using alpha particles as atomic bullets, probed the atoms in a piece of thin ( cm) gold foil. The nucleus was: very dense, very small and positively charged. also assumed electrons were located outside the nucleus. Ernest Rutherford gold foil

View of atomic Structure in early 1900’s 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.Niels Bohr

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 Increasing energy }

 n=quantum number  Only orbits where n =positive integer are permitted. Energy of quantized state = /n 2 Radius of allowed orbitals r n = n 2 ( nm) n = 1 n = 2E = -C (1/2 2 ) E = -C (1/1 2 )

Radius of electron orbits:  Another way:

Energy of one electron:  E: The ionization energy is equal to the negative energy of the electron

KE  The kinetic energy of the electron

Example:  Calculate the radius of the orbital associated with the energy level E 4 of the hydrogen atom.

Example:  Calculate the energy of the orbital associated with the energy level E 3 of the hydrogen atom.

Calculate  E for electrons in Hydrogen “falling” from n = 2 to n = 1 (higher to lower energy). n = 1 n = 2 Energy  E = E final - E initial = [(1/1 2 ) - (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 Energy - sign for  E indicates emission + for absorption since energy (λ, f) of light can only be + it is best to consider such calculations as  E = E upper - E lower n = 1 n = 2 Energy

The Bohr Model

 When an electron loses energy and drops to a lower state, a photon is released with energy:  E photon = hf =hc/ λ = E higher state –E lower state

E of photon:  Other ways:

The Bohr Model

The Ground State  The lowest energy state

Example:  An electron drops from the 4 th energy state to the 2 nd. 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)

Practice:  Complete The Bohr Atom Classwork  If you finish early, submit it and begin working on your homework

. n = 1 n = 2 Energy so, E of emitted light = (3/4)R = 2.47 x Hz ULTRAVIOLET and = c/ = 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 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 E Short Short High High Low E Long Long Low Low Energy Ultra Violet Lyman Infrared Paschen Visible Balmer E n = n n

Atomic Structure  Niels Bohr  Bohr model of the atom  Energy level diagrams

Bohr and Quantum Hypothesis  Discharge spectra  hf=E u – E i where E u 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 E 1 = -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 /  = x 107 (1 / / n2) where n = 3, 4, 5, 6,... Balmer found this by trial and error, and had no understanding of the physics underlying 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 the hydrogen atom as if it were an electron of charge -e orbiting in a circular path about a proton of charge +e.

Bohr Model

Review:

Energy Levels in Hydrogen Hydrogen atom explained

Energy Levels in Hydrogen E n = eV /n E 1 = eV E 2 = eV E 3 = eV E 4 = eV E 5 = eV E 6 = eV

Energy Transitions in Atoms Energy of photon = Energy lost by electron hf = E i - E f

Calculating Wavelengths of Emitted Light hf = E i - E f E 3 ---> E 2 : E i = eV E f = eV hf = (-3.40) = 1.89 eV = (1240 eV-nm) / E = 1240 / 1.89 = 656 nm

Review:  Wavelength corresponds to which characteristic of light??? Color!!!Color!!!

Balmer and Rydberg  Rydberg constant: The wavenumber 

Balmer Series Wavelength (nm) Relative Intensity TransitionColor > 2Violet > 2Violet > 2Violet > 2Violet > 2Violet > 2Bluegreen (cyan) > 2Red > 2Red

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 of visible wavelengths is approximately 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?

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:  duality-and-electron-energy-levels/revise-it/electron- energy-levels duality-and-electron-energy-levels/revise-it/electron- energy-levels  tml tml

By the end of class…  Two AP problems (review on the board)  Rubric (collected)  Guided note sheet (not collected)