Supplemental Slides for Chapter 2

Supplemental Slides for Chapter 2 • E = hu • Quantum numbers Electromagnetic Spectrum • Electromagnetic spectrum is illustrates the inverse relationship between frequency, wavelength and Energy. Reference credit: becuo.com Electromagnetic Energy Overview • What is a wave? • Any type of wave (e.g. water, light & sound) is a periodic movement or an oscillation that transports energy from on point to another. • Characteristics/Behaviors of waves: • Wave frequency, designated by the Greek letter, nu (n) • Units are “cycles per second (1/s or s-1) or a Hertz (Hz) • Wavelength is designated by the Greek letter, lambda (l) • Units in meters (m). • Amplitude is the height of the wave • = c or n = c/l Reference credit: alfa-img.com Electromagnetic Energy: n & l • The relationship between frequency & wavelength is INVERSE: • (a) Long wavelength → small frequency • Example: Visible light • (b) Short wavelength → high frequency • Example: Ultraviolet radiation • Mathematically: n = 1/l • The speed of a wave is the product of ln. • In a vacuum (i.e. space) ln is the speed of light (c) which is 2.998 x 108m/s. • Mathematically: n = c/l Reference credit: ww.m2c3.com • Energy relationship with frequency & wavelength • Radiation (light) having large l would have small values of energy (E). • Radiation (light) having small large l would have large values of energy (E). • Mathematically: E = hn or E = hc/l; where h is Planck’s constant A Look at E = hu • Max Planck work with blackbody radiation of objects lead to the discovery that absorb and emitted radiation energy (light) is proportional to its frequency (n) in distinct units called QUANTA (hn). • Mathematically this relationship can be described as: E = hn • Where h is Planck’s constant having a value of 6.6262 x 10-34 J·s Reference credit: chemwiki.ucdavis.edu Reference credit: becuo.com Energy Levels & Possible Electronic Transitions in the Hydrogen Atom Line Spectra • When particles absorb energy, eventually the energy is released as light. • It is released in discrete packets (hn) or quanta. • If this emitted energy is passed through a prism, a pattern of wavelengths specifically a line pattern, not a continuous spectrum of light as in a rainbow, is observed. • This pattern observed is called an emission spectrum. • Line spectra is used to identify the chemical substances (e.g. elements, molecules). • Each chemical species has a unique line spectra • See flame test interactive under Study Aids & Summaries (Module 5 – Chapter 4 in folio) Reference credit: www.astronoo.com Problem: Sodium metal (Na) has a energy equal to 3.78 × 10–19 J. 1. What minimum frequency of light is necessary to remove a surface electron from sodium? 2. To what wavelength of light (in nm) does this correspond? Useful information: E = hn Answer: Sodium metal (Na) has a energy equal to 3.78 × 10–19 J. 1. What minimum frequency of light is necessary to remove a surface electron from sodium? 2. To what wavelength of light (in nm) does this correspond? 1. 2. E 3.78 × 10−19 J 14 s −1 𝜈= = = 5.70 × 10 ℎ 6.626 × 10−34 J ∙ s 𝑐 𝜈 = 2.998×108 m/s 5.70×1014 s−1 = 5.26 × 10−7 m 9 1 × 10 nm −7 5.26 × 10 m × = 526 nm 1m Quantum Atom & Quantum Numbers • • Picture the quantum atom as having its nucleus as the center apex on a three-dimensional Cartesian (xyz axis) probability plot. Cartesian Coordinate Plot The four Quantum numbers (n, l, ml & ms ) describing the electron’s position relative to the atom’s nucleus on this plot • Each value describes an allowed energy state for an electron. • According to the Pauli Exclusion Principle no two electrons may have the same set of quantum numbers. • Each orbital type (l & ml) can only have TWO electrons with opposite spins. Reference credit: flickr.com The Four Quantum Numbers Name Symbol Allowed Values Examples Principal n Any positive integer 1, 2, 3, … Angular momentum Magnetic Spin ℓ mℓ ms Any integer from 0 to (𝑛 − 1) Any integer from −ℓ to + ℓ −1Τ2 or +1Τ2 Corresponds to The energy level 0, 1, 2 The type of sublevel or Orbital type (s, p, d, f..) −ℓ, …0, …+ℓ The placement/orientati on of orbital withing the x,y,z plot. −1Τ2, +1Τ2 The spin of the electron within a magnetic field Quantum Numbers: The electron’s address Principle quantum number (n) is the energy level (shell). • Its numerical values are n = 1, 2, 3, etc. Angular momentum (l) describes the orbital shape (subshell). • The numerical values of l are determined by the formula (n-1). • Level 1: Where n = 1 • : 1 -1 = 0 then s orbitals exist in level 1 and only s orbitals • Level 2: Where n = 2 • 2 – 1 = 1 indicating p orbitals can exist in level 2 • 1 – 1 = 0 indicating s orbitals also are present in level 2 • NOTE: To predict which types of atomic orbitals, exist within an energy level you use n – 1 = # until you reach the numerical value of zero. Reference: chem.libretexts Quantum Numbers: The electron’s address Orientation/magnetic quantum number (ml) indicates the axis location of the orbital; its placement within the xyz plot. • Its numerical values are determined by (+/-) value of l » ml explains why there is only 1 type of s orbital, but 3 types of p orbitals, 5 types of d orbitals & 7 types of f orbitals. Spin quantum number (ms) describes the spin of the electron in an orbital. • Electrons can spin with a magnetic field or against a magnetic field. » The numerical values for spin quantum number are either + ½ or – ½ Reference: chem.libretexts Quantum Numbers Summary Reference: Hyperphysics Quantum Calculations: How do you determine the types of orbitals allowed within each energy level To determine the type of orbitals (i.e., subshells) allowed (predicted) by Quantum Mechanics you need to know the energy level. • Example#1: • n = 1 (energy level 1) • The values of l (i.e., orbital shape quantum number) are calculated by subtracting 1 from n • n = 1 so 1-1 = 0 • The value 0 represents the orbital referred to as s • This indicates only s orbitals can exist in level 1. • Example#2: • If n = 2, the values of l would be: • 2-1 = 1; a l value of 1 refers to p orbital • 1-1 = 0; a l value of 0 refers to a s orbital • This indicates that in level 2 only s and p types orbitals can exist. Quantum Calculations: How do you determine the types of orbitals allowed within each energy level Summary: • To determine the types of atomic orbitals electrons can occupy in an energy level you need to know the energy level numerical value. • Example: n = 3 refers to the third energy level out from the nucleus. • Next, use the formula n – 1 = l (the quantum number associated with orbital or orbital shape) • Example: n = 4 • 4 – 1 = 3; the number 3 indicates a f type orbital • 3 - 1 = 2; the number 2 indicates a d type orbital • 2 - 1 = 1; the number 1 indicates a p type orbital • 1- 1 = 0; the number 0 indicates a s type orbital • Therefore, the types of atomic orbitals that electrons can occupy in the 4th energy level could be s, p, d or f type orbitals. Relationship between Quantum Numbers, n, l & ml Energy Predicted values Orbital shape Predicted values for ml Number level (n) for l designation (placement of orbital of orbitals ml = +/- l value (n-1) types per orbital, l Total number of orbital types in an energy level Possible number of electrons within an energy level 1 0 s 0 1 1 for s 2 for s 2 2 0 1 s p 0 -1, 0,+1 1 3 1 for s & 3 for p 2 for s & =4 6 for p = 8 electrons 3 3 3* 0 1 2 s p d 0 -1, 0, +1 -2, -1, 0 +1, +2 1 3 5 1 for s, 3 for p & 2 for s , 6 for p 5 for d = 9 & 10 for d = 18 electrons 4 4 4 4** 0 1 2 3 s p d f 0 -1, 0 +1 -2, -1, 0, +1, +2 -3, -2, -1, 0, +1, +2, +3 1 3 5 7 1 for s, 3 for p, 5 for d & 7 for f = 16 *3d orbitals do not appear until period 4 ** 4f orbitals do not appear until period 6 2 for s, 6 for p, 10 for d & 14 for f = 36 electrons Problem: 1. Determine the number and types of subshells when n = 3. 2. Calculate the total number of electrons that occupy when n = 2. 3. Identify these orbitals: a. b. Answer: 1. Determine the number and types of subshells when n = 3. n = 3 so l = (n-1) so can have: 2 (3-1) which are d orbital 1 (2-1) which are p orbitals 0 (1-1) which are s orbitals 2. Calculate the total number of electrons that occupy when n = 2. • When n = 2 you are in the 2nd period (2nd energy level) l values for n=2 would be: 2-1 = 1 so have p orbitals 1-1 = 0 so have s orbitals • ml = (+/-) l so have (-1, 0, 1) for p orbitals that means three orientations • Each orientation can have 2 electrons: 2 electrons x 3 = 6 electrons. • ml = (+/-) l so have (0) for s orbital meaning one orientation • Each orientation can have 2 electrons: 2 electrons x 1 = 2 electrons. Total number of electrons in n=2 level would be 8 electrons (6 + 2) Answer: 3. Identify these orbitals: a. This is an s orbital b. This is a p type orbital Problem: Identify the energy level and sublevel of any of the following sets of quantum numbers that are valid. n ℓ mℓ ms a. 1 0 0 0 b. 2 0 0 − 1ൗ2 c. 3 1 1 + 1ൗ2 d. 4 3 −3 + 1ൗ2 e. 3 −1 −1 + 1ൗ2 Level/sublevel Answer: Identify the energy level and sublevel of any of the following sets of quantum numbers that are valid. n ℓ mℓ ms Level/sublevel a. 1 0 0 0 Invalid ms b. 2 0 0 − 1ൗ2 2s c. 3 1 1 + 1ൗ2 3p d. 4 3 −3 + 1ൗ2 4f e. 3 −1 −1 + 1ൗ2 Invalid ℓ 22