The Bohr Model of the Hydrogen Atom

1. The Bohr Model of the Hydrogen Atom • In 1911, Rutherfords  - particle experiments were very controversial • The idea that all the positive charge of an atom was crammed into the nucleus was hard for many to accept • In 1913, Neils Bohr, a Danish physicist proposed: • That indeed all the positive charge was in the nucleus • The electrons orbited the nucleus much like planets orbit the sun continue…….

2. The Bohr Model of the Hydrogen Atom (cont) Bohr based his model of several well known facts at the time: 1. Visible light, x-rays, ultraviolet radiation, infrared radiation, microwaves and radio waves are all part of the electromagnetic spectrum Gamma Rays X-rays Ultraviolet Radio and Infrared Microwaves Television waves continue…….

3. The Bohr Model of the Hydrogen Atom (cont) 2. Waves can be described by the wave equation which includes velocity (c = speed of light), wavelength () and frequency () Wavelength: “ The distance between peaks of a wave “ Frequency: “ The number of wave cycles that pass a point each second. In units of cycles per second (cps) “ c =   or  = c/  continue…….

4. The Bohr Model of the Hydrogen Atom (cont) • 3. Light from the sun (white light) appears as a continuous • spectrum of light. • Continuous “ There are no discrete, individual • Spectrum of Light: wavelengths of light but rather all • wavelengths appear, one after • the other in a continuous fashion “ • When an element (hydrogen) is placed in a container • and heated or excited electrically the light emitted • forms a line spectrum of light • Line Spectrum of Light: “ Only certain wavelengths appear • and not others “ • This light is formed when a single element is heated • or excited and gives off discrete separate lines of color continue……. G 9.0 Electrons in Atoms, Periodic Table, Pt I

5. The Bohr Model of the Hydrogen Atom (cont) Hydrogen Line Spectrum Electrified Hydrogen Atoms Line Spectrum of Hydrogen continue……. 6

6. The Bohr Model of the Hydrogen Atom (cont) • 4. Light has both wave and particle like properties. • Its particle like properties are made up of individual • particle-like “packets” known as photons • The energy of a photon is directly • proportional to the frequency of the light • E = h  h = Planck’s constant • 5. Physics describes mathematical relationships among • radii, speed, energy and forces when one object moves • in an orbit around another continue……. G 9.0 Electrons in Atoms, Periodic Table, Pt I

7. The Bohr Model of the Hydrogen Atom (cont) Bohr boldly proposed that the energy possessed by an electron in a hydrogen atom and the radius of the orbit are quantized Quantized: “ Values limited to only specific values and not a continuous range of values “ The ramp is an example of a continuous situation in which any energy state is possible up the ramp Like a set of stairs, the energy states of an electron is quantized continue……. G 9.0 Electrons in Atoms, Periodic Table, Pt I

8. The Bohr Model of the Hydrogen Atom (cont) • Bohr proposed that the electron in the hydrogen atom has • quantized energy levels • This means that at any instant, the electron may have • one of several possible energies but at no time may • it have an energy between them Visible Series Infrared Series Ultraviolet Series continue……. 9

9. The Bohr Model of the Hydrogen Atom (cont) • The Energy Absorption Process: • “ Light or energy excites an electron from a lower energy level • (orbits in the Bohr theory) to a higher energy level “ • Since these energy levels are “ quantized “ and hence the electron can not ever be at any intermediate level, this means that the electron simply disappears from one orbit and reappears in another • This absorption or excitation process is called a quantum leap or quantum jump Quantum Jump: “ The quantized process by which an electron moves up or down from one energy level to another “ • The electron in a hydrogen atom is usually found in the “ ground state “ continue……. G 9.0 Electrons in Atoms, Periodic Table, Pt I

10. The Bohr Model of the Hydrogen Atom (cont) Ground State: “ The condition when all of the electrons in an atom occupy the lowest possible energy level “ What is a good analogy for this process? A spring and two balls The electron absorbs energy in the ground state and is excited to a higher level Both the atom and the electron now have higher energy This is an energy emission process and what we observe in the hydrogen line spectrum The Excited State The Ground State continue…….

11. The Bohr Model of the Hydrogen Atom (cont) The Excited State: “ The condition in which at least one electron in an atom is at an energy level above the ground state “ continue……. G 9.0 Electrons in Atoms, Periodic Table, Pt I

12. The Bohr Model of the Hydrogen Atom (cont) The atomic line spectral lines result when an electron in an excited state decays back to the ground state The electron loses energy, light is emitted and the electron returns to the ground state continue……. G 9.0 Electrons in Atoms, Periodic Table, Pt I

13. The Bohr Model of the Hydrogen Atom (cont) • The Bohr model works well for the hydrogen atom only • For elements larger than hydrogen the model • does not work • Never-the-less, Bohr made two huge contributions to the • development of modern atom theory • He suggested a reasonable explanation for the • atomic line spectra in terms of electron energies • He introduced the idea of quantized electron energy levels in the atom The Bohr atom lasted for about 13 years and was quickly replaced by the quantum mechanical model of the atom The Bohr model is a good starting point for understanding the quantum mechanical model of the atom continue……. G 9.0 Electrons in Atoms, Periodic Table, Pt I

14. The Quantum Mechanical Model of the Atom In 1924, Louis de Broglie, a French physicist suggested that all matter has both wave like properties and particle like properties Acceptance of the dual nature of matter and a principle called the uncertainty principle led to the development of Quantum Mechanics Uncertainty Principle: “ It is impossible to know simultaneously the exact position and momentum of an electron “ (Werner Heisenberg) Between 1925 and 1928 Erwin Schrodinger applied the principles of wave mechanics to atoms and developed the quantum mechanical model of the atom The model describes an atom that has certain allowed quantities of energy due to the wavelike motion of an electron whose exact location is impossible to know Rather than think of the electron as a particle orbiting a nucleus, now the electron is treated as a matter-wave in three dimensional space around the nucleus

15. The Quantum Mechanical Model of the Atom (cont) • A series of wave functions were developed by Schrodinger • to describe the motion of the electron’s matter-wave in • terms of time and position • Each solution to what is now called the Schrodinger • equation is associated with a given wave function, also • called an atomic orbital It is not possible to know precisely where the electron • is at any moment, but it is possible to describe where • it is most probable to find the electron • An equation called the square of the wave function • describes the possibility of finding the electron anywhere • in three dimensional space For any given energy level the electron probability can be expressed by an electron density diagram that describes an orbital continue……. G 9.0 Electrons in Atoms, Periodic Table, Pt I

16. An Atomic Orbital for the Hydrogen Electron Electron Density Diagrams: - Describing Atomic Orbitals Highest Electron Density Found Near the Nucleus The Nucleus The Electron “ Cloud “ or The Matter-Wave Structure of Electron Probability in 3-D Space. This describes the Shape of the Atomic Orbital continue……. G 9.0 Electrons in Atoms, Periodic Table, Pt I

17. Proper Name (Quantum No) Description The Quantum Numbers • The quantum mechanical model of the atom keeps the • quantized energy levels that Bohr introduced • The Quantum Mechanical Model uses four quantum • numbers to describe the electron energy 1) The Principle Energy Level (Shell) 2) The Sublevel (Subshell) 3) The Orbital 4) The Number of Electrons in an Orbital Principal Azimuthal Magnetic Electron Spin G 9.0 Electrons in Atoms, Periodic Table, Pt I

18. The Quantum Numbers (cont) • 1) The Principle Energy Level • The first quantum number • Electron Density • Extends in Three • Dimensional Space • Out From the Nucleus • The Higher Levels are further from the nucleus • The Higher Levels have higher energy • The Level Number Matches the Period Number on the Periodic Table The Principle Energy Levels are Identified by the Principle Quantum Number

19. Electrons in the first level ( shell, n 1 ) • have the lowest energy = = • Electrons in the second level ( shell, n 2 ) • have greater energy than those in the first level Each Principle Energy Level can Hold: 2n 2 Electrons The Quantum Numbers (cont) • 1) The Principle Energy Level (cont) • The principle energy level (shell) gets larger (their radius increases) as the principle quantum number n increases • As the principle level increases in size it can hold • more electrons that the level below it • The number of electrons a shell can hold is limited • by the equation Bohr developed: When an atom is being “built” the level that is filled first is the level with the lowest energy continue…….

20. The Quantum Numbers (cont) 1) The Principle Energy Level (cont) Maximum Electron Capacities of the First Four Principle Energy Levels (Shells) n = 4 2n2 = 2 x 42 = 32 electrons n = 3 2n2 = 2 x 32 = 18 electrons n = 2 2n2 = 2 x 22 = 8 electrons n = 1 2n2 = 2 x 11 = 2 electrons 58 electrons continue……. The Seventh Level is the Highest Occupied Ground-State Electrons in any Element now Known

21. The Quantum Numbers (cont) 2) The Sublevel (Subshell) • For each principal energy level there are one or • more sublevels (sometimes called subshells) • These are called the s, p, d and f sublevels • A specific sublevel is identified by both the principle energy level and the sublevel • The p sublevel in the second principle level is called the 2p sublevel • An electron in the 2p sublevel is called a “ 2p electron “ • The total number of sublevels within a given principle energy level is equal to n, the principal quantum number continue……. G 9.0 Electrons in Atoms, Periodic Table, Pt I

22. The Quantum Numbers (cont) 2) The Sublevel - (cont) Number of Sublevels Principal Energy Level Designation * n = 1 1 s n = 2 2 s, p n = 3 3 s, p, d n = 4 4 s, p, d, f n = 5 5 s, p, d, f n = 6 6 s, p, d, f * Designations beyond f are not needed for the elements known to date continue……. G 9.0 Electrons in Atoms, Periodic Table, Pt I

23. The Quantum Numbers (cont) 2) The Sublevel - (cont) • The energy of the sublevel increases in the order s, p, d, f at n = 2, the increasing order of energy is: 2s < 2p at n = 3, the increasing order of energy is: 3s < 3p < 3d at n = 4, the increasing order of energy is: 4s < 4p < 4d < 4f • Beginning with principle quantum level 3 and 4 the • energy ranges of overlap • The 3d electrons are higher in energy • than the 4s electrons continue……. G 9.0 Electrons in Atoms, Periodic Table, Pt I

24. Sublevel Designation s pdf 5 4 Relative Energies of Levels and Sublevels 3 2 1 Relative Energies for Levels and Sublevels • Not only do principal level have different energies (n levels), but sublevels have different energies ( s < p < d < f ) • The 3d sublevel is higher in energy than the 4s sublevel continue…….

25. The Quantum Numbers (cont) 3) The Orbital • Recall that it is not possible to know with certainty • both the energy and the position of an electron. • The quantum mechanical model of the atom does • allow for the calculation of where it is most • “ probable “ to find an electron • An orbital is described in terms of where it is most probable to find an electron in three dimensional space Orbital: “ The 3-dimensional region of space where it is most probable to find and electron “ continue……. G 9.0 Electrons in Atoms, Periodic Table, Pt I

26. The Quantum Numbers (cont) 3) The Orbital (cont) • Each Sublevel (s, p, d, f) has a certain number of orbitals The s sublevel One orbital The p sublevel Three orbitals The d sublevel Five orbitals The f sublevel Seven orbitals • All orbitals within a sublevel have the same energy continue……. G 9.0 Electrons in Atoms, Periodic Table, Pt I

27. z z z y x x y y x Pz Px Py The Quantum Numbers (cont) 3) The Orbital (cont) The s, p, d and f orbitals each have a certain shape s-Orbitals: All s-orbitals are spherical in shape p-Orbitals: All p-orbitals have the following shapes continue…….

28. The Quantum Numbers (cont) 3) The Orbital (cont) d-Orbitals: Have the following shapes continue…….

29. The Quantum Numbers (cont) 3) The Orbital (cont) f-Orbital: f-Orbitals are even more complicated One of the f orbitals There are 6 more f orbitals which are not shown continue……. Know the shape of the s and p Orbitals

30. The Quantum Numbers (cont) 4) The Number of Electrons in an Orbital Pauli Exclusion Principle: “ No two electrons can have the same combination of quantum numbers “ • The effect of this rule is to limit the number of • electrons in an orbital to two electrons maximum • An orbital may have: • No Electrons • One Electron • or, Two Electrons (but never more than two) continue……. G 9.0 Electrons in Atoms, Periodic Table, Pt I

31. Maximum Number of Electrons Sublevel Orbitals per Sublevel The Quantum Numbers (cont) Orbitals and Orbital Occupancy • An orbital may be occupied by 0, 1 or 2 electrons • The maximum number of electrons in a sublevel • is twice the number of orbitals in the sublevel s 1 1 x 2 e -= 2 e - p 3 3 x 2 e -= 6 e - d 5 5 x 2 e - = 10 e - f 7 7 x 2 e -= 14 e - continue……. G 9.0 Electrons in Atoms, Periodic Table, Pt I

32. The Quantum Numbers (cont) Orbital Occupancy vs Principal Energy Level Maximum Principal Number of Sublevels Number of Energy Level (n) Electron ( = 2n2) ( = n ) Electrons 1 2 s 2 s e- 2 8 s 2 s e- p 6 p e- 3 18 s 2 s e- p 6 p e- d 10 d e- 4 32 s 2 s e- p 6 p e- d 10 d e- f 14 f e- end……. G 9.0 Electrons in Atoms, Periodic Table, Pt I