1 Unit, Lesson : Answers to Homework Summary: The allowed values for quantum numbers for each principal quantum level n : n l m l m s corresponding sub-level number of orbitals in this sub-level n = s n = n =,, +,, +,,, +, +,, +,,, +, +,,,, +, +, + s p s p d 4s 4p 4d 4f 7 eg. As: s s p 6 s p 6 4s d 4p or [Ar] 4s d 4p s s p x p y p z s p x p y p z 4s d yz d xz d xy d z d x-y 4p x 4p y 4p z s n = l = m l = n = l = m l = n = l = m l = + n = l = m l = - m s = -½ l = m l = 9Cu s s p 6 s p 6 4s d or [Ar] 4s d s s p x p y p z s p x p y p z 4s d yz d xz d xy d z d x-y 4p x 4p y 4p z s n = l = m l = n = l = m l = + l = m l = n = l = m l = -
2 Unit, Lesson : Homework on Quantum Numbers. Write the quantum numbers that represent the following electrons: a) a p electron would be given the quantum numbers: n =, l =, m l = + and m s = + ½ b) a s electron would be given the quantum numbers: n =, l =, m l = and c) a 4f 6 electron would be given the quantum numbers:, l =, m l = + and m s = + ½. What are the allowable (possible) values for l when: a) : l can be,, or (s, p, d or f) b) n = : l can be,, or (s, p or d) c) n = : l can be (s) d) n = : l can be,,, or 4 (s, p, d, f or g). What are the allowable (possible) values for m l when: a), l = : m l can be -, -, -,, +, +, + b) n =, l = : m l can be -,, + c) n =, l = : m l can be d) n =, l = 4: m l can be -4, -, -, -,, +, +, +, Write the principal quantum number and letter indicating orbital shape for each of the following: a) n =, l = means p c), l = means 4f e), l = means 4p b) n =, l = means d d) n =, l = means s f) n =, l = means s. State whether the following sets of quantum numbers are possible ( ) or impossible (X): a) n =, l =, m l = - and m s = + ½ no, when n = then l has a maximum value of (s, p or d) b) n =, l =, m l = - and yes, this is the same as the d 7 electron c) n =, l =, m l = and yes, this is the same as the s electron d) n =, l =, m l = and m s = no, m s must be either + ½ or ½ e) n =, l =, m l = + and m s = + ½ no, when l = (s) then the orientation m l must also be f) n =, l =, m l = and m s = + ½ no, n can not be g), l =, m l = + and m s = + ½ yes, this is the same as the 4p electron h) n =, l =, m l = - and no, when l = (p) then the orientation m l can be, or +
3 . Read pages 8.. On page 6, answer questions. Unit, Lesson : Answers to Homework Question : What are the allowed values for l in each of the following cases? a) n = the allowed values for l are ( n-), so l can be,,,, 4 (double check: when n =, there are types of orbitals: s, p, d, f, g) b) n = the allowed values for l are ( n-), so l can be (double check: when n =, there is type of orbital: s) Question : What are the allowed values for m l for an electron with the following quantum numbers? a) l = 4 the allowed values for ml are (-l +l), so ml can be 4, -, -, -,, +, +, +, +4 (double check: l = 4 means the same as the g sublevel, which can have 9 orbitals) b) l = the allowed values for m l are (-l +l), so m l can only be (double check: l = means the same as the s sublevel, which can have orbital) Question : What are the names, ml values and total number of orbitals described by the following quantum numbers? a) n =, l = this represents the second principal quantum level (n=), and the s orbital: s -there is only one ml value: because this represents only one orbital b), l = this represents the fourth principal quantum level (), and the f orbitals: 4f -there are 7 ml values: -, -, -,, +, +, + so this represents 7 orbitals Question 4: Determine the n, l and possible ml values for an electron in the p orbital -the p orbital is in n = - p orbitals are indicated by l = -when l =, the allowed values for ml are,, + Question : Which of the following are allowable sets of quantum numbers for an orbital? Explain. a), l = 4, ml = this is not allowable because l can only have values up to (n - ) b) n =, l =, ml = this is allowable, l is less than n and ml can be any of, -,, +, + c) n =, l =, ml = this is allowable, l is less than n and ml can only be d) n =, l =, ml = -4 this is not allowable; ml can only have values,, -,, +, +, +. On page 8, answer questions,,, 6. Question : Quantum Number and Description symbol What it Describes. The Principal Quantum Number (n): the allowed values for n are,, infinity. The Orbital Shape or Angular Momentum Quantum Number (l): the allowed values for l are,,, (n ). The Magnetic Quantum Number (m l ): the allowed values for m l are l. + l n describes the size of the quantum level or how far the electrons are from the nucleus (their energy) l the shape of the energy sub-levels (types of orbitals) within each principal quantum level m l indicates the three dimensional orientation of an electron
4 Question : n l ml,, +,,, +, +,,,, +, +, + 4s 4p 4d 4f 7 Question : Identify any values that are incorrect: a) n =, l =, ml =, name p When n =, the only allowable value for l is, which means ml is also and indicates a s orbital b), l =, ml = +, name 4d The quantum numbers are correct, but the name is not. When l =, it indicates an f orbital, not d. c) c) n =, l =, ml = -, name p The first two quantum numbers are correct and agree with the name. The value for ml is impossible: the allowed values when l = are,, +. Question 6: a), l =, ml =, name 4p b) n =, l =, ml =, name p c) n =, l =, ml = -, name d d) n =, l =, ml =, name s 4. Read pages 47.. To see how electron configurations are related to an element s position on the periodic table, write the name of the last valence electron of each element (eg. d ) in the appropriate square of the Periodic Table below. Use the predicted electron configurations for Cr, Mo, W, Cu, Ag and Au. See next page
5 6. On the Periodic Table below, label the: a) Group numbers and Periods b) s,p,d and f blocks of elements c) the transition elements and inner-transition elements d) Noble gases, Alkali metals, Alkaline Earth metals, and Halogens Period Group : s s 4 6 Alkali metals Alkaline Earth metals Halogens s s p p p p 4 p p 6 s s Transition Elements (d block) p p p p 4 p p 6 4s 4s d d d d 4 d d 6 d 7 d 8 d 9 d 4p 4p 4p 4p 4 4p 4p 6 s s 4d 4d 4d 4d 4 4d 4d 6 4d 7 4d 8 4d 9 4d p p p p 4 p p 6 6s 6s d d d d 4 d d 6 d 7 d 8 d 9 d 6p 6p 6p 6p 4 6p 6p 6 7s 7s 6d 6d 6d 6d 4 6d 6d 6 6d 7 6d 8 6d 9 6d 7p 7p 7p 7p 4 7p 7p 6 Noble gases Inner Transition Elements (f block) 4f 4f 4f 4f 4 4f 4f 6 4f 7 4f 8 4f 9 4f 4f 4f 4f 4f 4 f f f f 4 f f 6 f 7 f 8 f 9 f f f f f 4 7. On the page Nuclear Charge and the Shielding Effect: Explaining the Trends on the Periodic Table (handed out in class), for each element complete the: a) electron configuration b) Rutherford-Bohr diagram c) Nuclear charge (the number of protons in the nucleus = atomic number = Z) d) Shielding effect (the number of electrons in the full shells between the nucleus and the valence shell) e) Net Nuclear attraction (the nuclear charge subtract the shielding effect). Net nuclear attraction is the effective (Z eff ) or actual attraction that exists between a valence electron and the nucleus. f) Use the numbers on the back of your Periodic Table to complete the ionization energy (First Ionization Potential, V), electronegativity and Atomic Radius (, Angstroms) Bring the completed sheet to class for our next lesson! Shielding Effect
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