1. Chapter 4 Arrangement of Electrons in Atoms

2. Section 1 The Development of a New Atomic Model

3. The New Atomic Model
The previous models we studied did not explain where electrons were located.
A new atomic model revealed a relationship between light and an atom’s electrons.
We used to think of light as a wave. Light acts like a wave, but has particle-like characteristics as well.

4. The Wave Description of Light
Visible light is a type of electromagnetic radiation, a form of energy that exhibits wavelike behavior as it travels through space.
Visible light, x rays, ultraviolet light, infrared, microwaves, and radio waves make up the electromagnetic spectrum.

6. The Wave Description of Light
Wave motion involves wavelength and frequency.
Wavelength is the distance between corresponding points on adjacent waves.
Frequency is the number of waves that pass a given point in a specific time, usually one second. Frequency is measured in hertz.
HIGH FREQUENCY
LOW FREQUENCY

7. Frequency and Wavelength
Frequency and wavelength are related mathematically:
c= λv, where c= speed of light, λ= wavelength, and v= frequency of the electromagnetic wave
Since c is a constant, the product of λv is constant too.
c= λv

8. Photoelectric Effect
The photoelectric effect refers to the emission of electrons from a metal when light shines on the metal.
For a given metal, no electrons were emitted if the light’s frequency was below a certain minimum, no matter how long the light was shone. If light was a wave, it would be able to knock loose an electron from the metal. We couldn’t explain why there must be a minimum frequency in order for this effect to take place.

9. Planck’s Explanation
German physicist Max Planck suggested that a hot object emits energy in small, specific amounts called quanta (plural for quantum).
A quantum is the minimum quantity of energy that can be lost or gained by an atom.

10. The Particle Description of Light
Planck proposed the following relationship between a quantum of energy and the frequency of radiation.
Where E = energy (in Joules), v = frequency of the radiation emitted, and h is Planck’s constant, which is always x J·s.
E = hv

11. The Particle Description of Light
Einstein expanded this theory by saying that electromagnetic radiation has a dual wave-particle nature.
Light exhibits many wavelike features, but also acts like a stream of particles.
Each particle, or “photon,” of light carries a quantum of energy.
A photon is a particle of electromagnetic radiation having 0 mass and carrying a quantum of energy.

12. Einstein’s Photons E = h v
According to this equation, the minimum energy for an electron to be ejected from a metal surface depends on the minimum frequency.

13. The Hydrogen-Atom Line-Emission Spectrum
When current is passed through a gas at low pressure, the potential energy of some of the gas atoms increases.
The lowest energy state of an atom is its ground state.
A state in which an atom has a higher potential energy than it has in its ground state is an excited state.
When an excited atom returns to ground state, it gives off light.

14. What a Bright Idea!
Excited neon atoms produce light when they fall back to a lower energy excited state or the ground state.

15. Line-Emission Spectrum
When a narrow beam of the emitted light was shined through a prism, it was separated into a series of specific frequencies (and therefore specific wavelengths, λ = c/v) of visible light.
The line-emission spectrum of an element is a series of wavelengths of emitted light created when the visible portion of light from excited atoms is shined through a prism.

16. Line Spectra for Hydrogen, Mercury, and NeonHg Ne

17. Hydrogen’s Line-Emission Spectrum
Scientists expected to observe a continuous spectrum when they observed hydrogen through the spectrum, but they only saw a few select colors.
A continuous spectrum is the emission of a continuous range of frequencies of electromagnetic radiation.
An example of this is a rainbow.

18. The Perplexing Electron of Hydrogen
Scientists were confused at why hydrogen only emits specific frequencies when current passes through it.
This suggested that the electron of a hydrogen atom exists only in very specific energy states.
If an atom at excited state (E2) falls back to ground state (E1), it releases a photon that has energy:
E2-E1=Ephoton= hv

19. Bohr to the Rescue!
Danish physicist Niels Bohr proposed a model of the hydrogen atom that linked the atom’s electron with photon emission.

20. Atoms Aren’t Bohr-ing! Bohr’s model of the atom says:
The electron can circle the nucleus only in allowed paths, or orbits.
When the electron is in one of these orbits, the atom has a definite, fixed energy.
The electron, and the atom as well, is in its lowest energy state when the electron is in the orbit closest to the nucleus.
The orbit is separated from the nucleus by a large empty space where the electron can not exist.

21. How Does This Explain the Lines?
While an electron is in an orbit, it can neither lose or gain energy, but it can move to a higher energy orbit by gaining an amount of energy equal to the difference in energy between the higher-energy orbit and the initial lower-energy orbit.
When hydrogen is in an excited state, its electron is in a higher-energy orbit.

22. How Does This Explain the Lines?
When the atom falls back from the excited state, the electron drops down to a lower-energy orbit.
In the process, a photon is emitted that has an energy equal to the energy difference between E2-E1.
Photons are absorbed when the electron moves to a higher energy orbit.
Photons are emitted when electrons move to a lower-energy orbit.

23. Section 2 Quantum Model of the Atom

24. A. Electrons as Waves Louis de Broglie (1924)
Applied wave-particle theory to e-
e- exhibit wave properties
QUANTIZED WAVELENGTHS

25. A. Electrons as Waves
QUANTIZED WAVELENGTHS

26. A. Electrons as Waves EVIDENCE: DIFFRACTION PATTERNS VISIBLE LIGHT

27. B. Quantum Mechanics Heisenberg Uncertainty Principle
Impossible to know both the velocity and position of an electron at the same time

28. B. Quantum Mechanics Schrödinger Wave Equation (1926)
defines probability of finding an e-
mathematically describes the wave
properties of electrons and other very
small particles.

29. Radial Distribution Curve
B. Quantum Mechanics
Orbital (“electron cloud”)
Region in space where there is 90% probability of finding an e-
Orbital
Radial Distribution Curve

30. C. Quantum Numbers Four Quantum Numbers:
Specify the “address” of each electron in an atom
UPPER LEVEL

31. C. Quantum Numbers s p Shape of the orbitals: Energy Sub-level
Spherical shape (circle)
Lowest level
Holds 2 electrons MAX p
Dumb bell Shape
Second Sub level
Holds 6 electrons MAX

32. C. Quantum Numbers d f Double Dumb bell Shape Higher Electron Levels
Holds 10 electrons MAX f
Flower Shape
Highest Electron Levels
Holds 14 electrons MAX

33. C. Quantum Numbers px py pz

34. C. Quantum Numbers 2s 2px 2py 2pz
Orbitals combine to form a spherical shape. 2s
2pz
2py
2px

35. C. Quantum Numbers 4. Spin Quantum Number ( ms )
Electron spin  +½ or -½
An orbital can hold 2 electrons that spin in opposite directions.

36. Section 3 Arrangement of Electrons in Atoms

37. Electron Configurations
the arrangement of electrons in an atom
each type of atom has a unique electron configuration
electrons tend to assume positions that create the lowest possible energy for atom
ground state electron configuration- lowest energy arrangement of electrons

38. C. Quantum Numbers Pauli Exclusion Principle
No two electrons in an atom can have the same spin (or location).
Each e- has a unique “address”:
1. Principal # 
2. Ang. Mom. # 
3. Magnetic # 
4. Spin # 
energy level
sublevel (s,p,d,f)
orbital
electron

39. Rules for Arrangements
Aufbau Principle-
an electron occupies the lowest-energy orbital that can receive it
Always start at “s”

40. Rules for Arrangements
Hund’s Rule-
orbitals of equal energy are each occupied by ONE electron before any orbital is occupied by a second
all unpaired electrons must have the same spin

41. Rules for Arrangements

42. Writing Configurations
Start by finding the number of electrons in the atom
Identify the sublevel that the last electron added is in by looking at the location in periodic table
Draw out lines for each orbital beginning with 1s and ending with the sublevel identified
Add arrows individually to the orbitals until all electrons have been drawn

43. Writing Configurations
Orbital Notation:
an orbital is written as a line
each orbital has a name written below it
electrons are drawn as arrows (up and down)
Electron Configuration Notation
number of electrons in sublevel is added as a superscript

44. Order for Filling Sublevels

45. Silicon number of electrons: 14 last electron is in sublevel: 3p
1s 2s p s p
Valence Electrons- the electrons in the outermost energy level

46. Sodium number of electrons: 11 last electron is in sublevel: 3s
1s2 2s2 2p6 3s1
1s s p 3s

47. Calcium number of electrons: 20 last electron is in sublevel: 4s
1s2 2s2 2p6 3s2 3p6 4s2
1s s p 3s
3p 4s

48. Bromine number of electrons: 35 last electron is in sublevel: 4p
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p5
1s s p 3s 3p
1s s p 3s 3p
4s 3d p
4s 3d p

49. Argon number of electrons: 18 last electron is in sublevel: 3p
1s2 2s2 2p6 3s2 3p6
1s s p 3s 3p

50. Noble Gas Notation short hand for larger atoms
configuration for the last noble gas is abbreviated by the noble gas’s symbol in brackets