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AWhy does the method of separation of variables work better for problems like the hydrogen atom when done in spherical coordinates (r, 0 , 0) than it does when you work in Cartesian coordinate (x.y,z)? A) Because Schrodinger's equation treats the three directions (x,y,) completely differently, while it treats (r, 0 , 6) all the same B) Because the derivative terms in spherical coordinates are independent on each other C) Because the energy term only gets simpler in spherical, not Cartesian coordinates D) Because Schrodinger's equation is naturally written in spherical coordinates

AWhy does the method of separation of variables work better for problems like the hydrogen atom when done in spherical coordinates (r, 0 , 0) than it does when you work in Cartesian coordinate (x.y,z)? A) Because Schrodinger's equation treats the three directions (x,y,) completely differently, while it treats (r, 0 , 6) all the same B) Because the derivative terms in spherical coordinates are independent on each other C) Because the energy term only gets simpler in spherical, not Cartesian coordinates D) Because Schrodinger's equation is naturally written in spherical coordinates

Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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6-THE MOST CORRECT ANSWER: Why does the method of separation of variables work better for problems like the hydrogen atom when done in spherical coordinates (r, 6 , 0 ) than it does when you work in Cartesian coordinate (xy,z)? A) Because Schrodinger's equation treats the three directions (x,y,) completely differently, while it treats (r, 0, 6) all the same B) Because the derivative terms in spherical coordinates are independent on each other ) Because the energy term only gets simpler in spherical, not Cartesian coordinates D) Because Schrodinger's equation is naturally written in spherical coordinates An class we divided up the hydrogen atom into a radial function R (r) and an angular function Y (0, 6). Under what circumstances can we reuse these functions Y(6, $) on another problem? A) They can be used on any problem in 3D, and they are always exactly the same B) They can be used on any problem in 3D, though their functional form will change C) They can be used on any spherically symmetric problem, and they are always exactly the same D) They are worked out and can only be used for hydrogen-like atoms 3 Which of the following statements about the hydrogen atom ground state is INCORRECT? A) It is described by the quantum numbers n = 1, f = 0, m = 0. B) The electron's angular momentum equals h/2r. C) The wave function is spherically symmetrical. D) The radial distribution function has its maximum at the Bohr radius ao.
Transcribed Image Text:6-THE MOST CORRECT ANSWER: Why does the method of separation of variables work better for problems like the hydrogen atom when done in spherical coordinates (r, 6 , 0 ) than it does when you work in Cartesian coordinate (xy,z)? A) Because Schrodinger's equation treats the three directions (x,y,) completely differently, while it treats (r, 0, 6) all the same B) Because the derivative terms in spherical coordinates are independent on each other ) Because the energy term only gets simpler in spherical, not Cartesian coordinates D) Because Schrodinger's equation is naturally written in spherical coordinates An class we divided up the hydrogen atom into a radial function R (r) and an angular function Y (0, 6). Under what circumstances can we reuse these functions Y(6, $) on another problem? A) They can be used on any problem in 3D, and they are always exactly the same B) They can be used on any problem in 3D, though their functional form will change C) They can be used on any spherically symmetric problem, and they are always exactly the same D) They are worked out and can only be used for hydrogen-like atoms 3 Which of the following statements about the hydrogen atom ground state is INCORRECT? A) It is described by the quantum numbers n = 1, f = 0, m = 0. B) The electron's angular momentum equals h/2r. C) The wave function is spherically symmetrical. D) The radial distribution function has its maximum at the Bohr radius ao.
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