chem216hw3-1 - The principle quantum number n cannot be...

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Chem 2160 HW3 Answer Key February 9, 2009 1. The potential is separable: V ( x,y ) = V ( x ) + V ( y ), so Ψ( x,y ) = ψ x ( x ) ψ y ( y ) = r 4 L x L y p sin n x π ¯ h L x x Pp sin n y π ¯ h L y y P where n x and n y are the quantum numbers. 2. (a) 3 s i. M 6 M 4 M 2 0 2 4 6 M 6 M 4 M 2 0 2 4 6 ii. 5 10 15 20 0.5 1.0 1.5 2.0 2.5 3.0 iii. 5 10 15 20 0.1 0.2 0.3 0.4 0.5 0.6 0.7 (b) 3 p x 1
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i. M 20 M 10 0 10 20 M 20 M 10 0 10 20 ii. 5 10 15 20 M 0.5 0.5 1.0 1.5 iii. 5 10 15 20 0.5 1.0 1.5 2.0 2.5 3.0 (c) 3 d xy i. M 20 M 10 0 10 20 M 20 M 10 0 10 20 ii. 5 10 15 20 0.5 1.0 1.5 2.0 2
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iii. 5 10 15 20 1 2 3 4 3. (a) E = Ry p 1 n 2 i - 1 n 2 f P , where 1 Ry = 13 . 6 eV. Thus, E 1 s 2 p = Ry ( 1 1 2 - 1 2 2 ) = 10 . 2 eV. (b) 12.1 eV (c) 12.8 eV (d) As the principal quantum number increases, the electron is on average farther away from the nucleus. Eventually, the atom is ionized as the electron Fnds itself “at inFnity.” 4. Possible answers might include: The conFned electron cannot have zero kinetic energy; it is a standing wave (that is, in an orbital). The electron in a central potential has zero-point energy.
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Unformatted text preview: The principle quantum number n cannot be zerothis would indicate the electron does not exist. Basically, you have to cite something quantum mechanical. 5. 12.54 Zumdahl b is not allowed, because | m l | > l c is not allowed, because n = 0. d is not allowed, because | l | < 6. 12.60 Zumdahl. Along a lobe (the x-axis in the Fgures) the wavefunction will be proportional to the radial part. You already have a picture of the square of the radial part of the 3 p orbital from question 2. The graph for the 2 p orbital will have one fewer node (or one fewer peak). 3...
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This note was uploaded on 02/23/2009 for the course CHEM 2160 taught by Professor Lee, s during the Spring '08 term at Cornell University (Engineering School).

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chem216hw3-1 - The principle quantum number n cannot be...

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