University:
University of Houston
Course:
PHYS 4356 | Particle and Nuclear Physics
Academic year:

2022
Views:

408

Pages:

9
Author:

Pierce Valdez

•Each subshell is designated by a letter: • l = 0 indicates an s subshell. • l = 1 indicates a p subshell. • l = 2 indicates a d subshell. • l = 3 indicates an f subshell. • Subshells are named by using the n value and the letter designation. The subshell with n = 2 and l = 0 is called the 2s subshell. The only orbital in the 2s subshell has n = 2, l = 0, and m l = 0. The subshell with n = 3 and l = 1 is the 3p subshell. It has three orbitals: n = 3, l = 1, and m l = +1, 0 and –1. •Each of an atom’s orbitals is specified by a set of n, l, and m l values. •These fix the orbital’s size, energy, shape, and spatial orientation. 36 Skill 7-5. Determining quantum numbers and sublevel designations Problem: Give the name, magnetic quantum numbers, and number of orbitals for each subshell with the quantum numbers shown: (a) n = 3, l = 2 (b) n = 2, l = 0 (c) n = 5, l = 1 (d) n = 4, l = 3 Solution: (a) (b) (c) (d) n l 3 2 2 0 5 1 4 3 subshell name 3d 2s 5p 4f possible m l No. of orb. -2, -1, 0, +1, +2 5 0 1 -1, 0, +1 3 -3, -2, -1, 0, +1, +2, +3 7 37 Identifying Incorrect Quantum Numbers Problem: What is wrong with each of the following quantum number designations and/or subshell names? Solution: (a) A sublevel of n = 1 can have only l = 0, not l = 1. The only possible subshell is 1s. (b) A subshell with l = 3 is an f subshell, not a d subshell. The subshell name should be 4f. (c) A subshell with l = 1 can have only m l of -1, 0, +1, not -2. 38 Concept 7-12. The shapes and nodes of s, p, and d orbitals • Each subshell of the H atom has orbitals with a characteristic shape. s orbitals ( l = 0) are spherically symmetrical around the nucleus. nodes (ψ 2 = 0) 1s 2s 3s 39 • The p orbital (with l = 1) has two regions of higher probability that lie on either side of the nucleus. • The nucleus lies at a nodal plane of p orbitals. • The max. value of l is n –1, so only shells with n ≥ 2 can have p orbitals. • Energies of p orbitals: 2p < 3p < 4p... Simplified p orbital shape 40 •The three possible m l values: +1, 0, and –1, which lead to three mutually perpendicular p orbitals. px py pz • The three p orbitals are equivalent in size, shape, and energy, differing only in orientation. 41 The d orbitals • Orbitals with l = 2 are called d orbitals. There are five possible m l values for the l = 2 sublevel: +2, +1, 0, –1, and –2. • d orbitals can have any one of five different orientations. Actual shape of d yz simplified shape of d yz 42 • In accord with the quantum number rules, a d orbital must have a principal quantum number of at least n = 3. • The 4d orbitals extend farther from the nucleus than the 3d, and the 5d orbitals extend still farther. 43 Energy Levels of the Hydrogen Atom •In the ground state the electron is in the n = 1 shell (1s orbital) n = 4 (4s, 4p, 4d, 4f) n = 3 (3s, 3p, 3d) •Photons of the correct energies can promote the electron to higher shells. n = 2 (2s, 2p) •The excited atom can return to the ground state by emitting a photon of the same energy. n = 1 (1s) Energy 44