Line Spectra and the Bohr Model

Flame Test Colors

• Color’s are emitted when atoms are given energy

• The actual color seen is a mixture of many colors

Atomic Emission Spectrum

Atoms Give Off Colors of Light

• AES: The set of frequencies (colors of light) emitted by atoms of an element

• Each element’s atomic emission spectrum is unique (Fingerprint of the element)

• Line Spectrumhttp://www.colorado.edu/physics/2000/quantumzone/index.html

Observing the Spectrum• Spectrascope: Acts like a prism to

split light into its actual colors– Our eye sees the colors given off all

mixed together– 2 colors could look the same to us,

but have vastly different “line spectra”

Bohr’s Model of the Atom• Atom has distinct energy levels,

(Orbits) starting with n=1 then n=2, n=3…

• Ground State: lowest energy level• When excited, it jumps to a higher

state (excited state)

• When it goes back down, it emits energy (light)– ‘Step ladder’

Small orbit = low energy stateLarge orbit = high energy state

Bohr’s Line Spectra• Energy of light given off is due to how

far the electron is ‘falling’ through levels– Not all of it is visible

• Different jumps give different wavelengths

• Grouped in “series”– Lyman series: Emits light in the UV region– Balmer series: Emits light in the visible

spectrum– Paschen series: Emits light in the IR

region

Figure 4.16 – Prentice Hall Chemistry

Glowing• Other ways electrons emit light:

– Fluorescence • Atoms in the molecule absorb certain

wavelengths of light and emit it back out• Demo: Needs UV light to absorb/emit• The reaction is FAST

– Photoluminescence (foh-tuh-loo-muh-nes-uh ns)

• Atoms absorb wavelengths of light and emit – however the reaction is SLOW

• Charging your glowing object– Chemiluminescence

• Glowsticks

Electrons act like waves?• Louis de Broglie

– Radiant Energy waves (light) behave like a particle…. Could the opposite be true?

• Particles act like waves?– Predicted that all moving matter has

wave characteristics based on it’s velocity and mass

– Works for all matter traveling at speed v, only relevant to electrons however

=hmv

De Broglie Waves- What is the wavelength of an electron

moving with a speed of 5.97 x 106 m/s? - (The mass of the electron is 9.11 x 10–

28 g)

- Basis for electronmicroscope

Modern Quantum Theory of Electrons

Probability and Orbitals

Werner Heisenberg• Heisenberg’s Uncertainty Principle

- It is impossible to know both exact speed and location of an electron

Bohr wasn’t right…• Bohr’s equations only

worked for hydrogen atoms – (1 electron)

• Too simple!

2 important Bohr ideas:1. Electrons exist only in certain discrete energy levels (described by their quantum #’s)2. energy is involved in moving an electron from one level to another

Quantum TheoryWhat do people think….

• Niels Bohr:“Fundamentally incomprehensible”

• Richard Feynman (nobel prize winner)“If you think you understand quantum

mechanics, you don’t understand quantum mechanics”

Describing Electrons using Orbitals• Atomic Orbital:

– A region around the nucleus of an atom where an electron with a given energy is likely to be found

– Different from ORBIT (the circular ring)

Orbitals• Unlike Bohr’s model, the orbital

makes no attempt to describe the electron’s path

• Recall Bohr’s levels (quantum #’s: n=1, n=2, …)

• Orbital Theory does the same but has 3 quantum #’s– N, l, ml

The 3 Quantum #’s1) Principal Quantum Number N•Can have a positive integer value n=1, 2, 3, etc•As n increases, the orbital gets larger and increases in energy

2) Azimuthal Quantum Number L (subshell)•Can have integral values from 0 to n-1 for each value of n•Defines the shape of the orbital

3) Magnetic Quantum Number Ml (orbital)•Has integral value from -L to L

Value of L 0 1 2 3

Letter used

S P D F

Sounds very confusing…• Where do you live?

– State, City, Street Name, House #• Electrons are identified the same

way..– Principle energy level, sublevel,

orbital

1. Principle energy levels (1,2,3…)2. Sublevel (s, p, d, f)3. Orbitals

Values of N, L, and MlTextbook problems 6.49-6.54

Within the sublevels…• S has 1 orbital

• P has 3 orbitals

• D has 5 orbitals

• F has 7 orbitals

– 2 electrons can fit in each orbital (box)

Why?

(a) Predict the number of subshells in the fourth shell, that is, for n = 4. (b) Give the label for each of these subshells. (c) How many orbitals are in each of these subshells?

• Solution • (a) There are four subshells in the fourth shell,

corresponding to the four possible values of l (0, 1, 2, and 3).

• (b) These subshells are labeled 4s, 4p, 4d, and 4f. • (c)

– There is one 4s orbital (when l = 0, there is only one possible value of ml: 0).

– There are three 4p orbitals (when l = 1, there are three possible values of ml: 1, 0, and –1).

– There are five 4d orbitals (when l = 2, there are five allowed values of ml: 2, 1, 0, –1, –2).

– There are seven 4f orbitals (when l = 3, there are seven permitted values of ml: 3, 2, 1, 0, –1, –2, –3).

SAMPLE EXERCISE 6.6 Subshells

Principle Energy Level• How many sublevels are there in

each energy level?– N=1 has 1 sublevel (s)

• 1s– N=2 has 2 sublevels (s and p)

• 2s & 2p– N=3 has 3 sublevels (s, p, and d)

• 3s, 3p, & 3d– N=4 has 4 sublevels (s, p, d, and f)

• 4s, 4p, 4d, & 4f

Practice Exercise 2(a) What is the designation for the subshell with n = 5 and l = 1? (b) How many orbitals are in this subshell? (c) Indicate the values of ml for each of these orbitals.

Answers: (a) 5p; (b) 3; (c) 1, 0, –1

Radial Probability Functions• The probability that an electron

(with a certain energy) will be a distance “r” from the nucleus

Node

Shapes of orbitals• S orbital

– “Sphere”

• P orbital– “Dumbbell”

• D orbital– “Flower”

What happens to the sphere as “n”

gets bigger?

Quiz on Friday!!• Shapes of orbitals

– Know what they are– Draw the s, p, and d orbitals

• Quantum #’s questions– Be able to determine & write them

Check-Up Questions• Give the numerical values of n and

l for each:– A) 2p– B) 2s– C) 4f– D) 5d

• Solution:– A) n=2, l=1– B) n=2, l=0– C) n=4, l=3– D) n=5, l=2

Sample Test Questions…1) The __________ quantum number defines the shape of an

orbital.• a) spin• b) magnetic• c) principal• d) azimuthal• e) psi

2) The n = 1 shell contains ___ orientations of p orbitals. All the other shells contain ___ orientations of p orbitals.

• a) 3, 6-9• b) 0,3• c) 6,2• d) 3,3• e) 2,6

3) In a px orbital, the subscripts x denotes the __________ of the orbital.

• a) energy• b) spin of the electrons• c) probability of the shell• d) size of the orbital• e) axis along which the orbital is aligned

Fillin’ ‘em up with electrons• Aufbau Principle

– Add one electron at a time to the lowest energy level available

• The 4th Quantum # (sorry)– Ms

describes the “spin” of an electron– Possible values: +½ or –½

• Pauli Exclusion Principle– No two electrons in an atom can have

the same set of four quantum numbers (n, l, ml, and ms)

– This means no more than 2 electrons per orbital

Using Pauli…

What is the set of quantum #’s for the last electron?

N=2, L=0, Ml=0, Ms= +½

Electron Configurations• The way electrons are distributed

among orbitals• Ground state: most stable

electron configuration• If not for Pauli, they would all

crowd the 1s… but they can’t

• The levels will fill up by lowest energy first (electrons are lazy)

Energy of each level

EN

ER

GY

1s

2s

3p3p 3p

2p2p 2p

3s

4s

3d3d 3d 3d 3d

4p4p 4p

Sneaky!