/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q46E In Table 7.5, the pattern that d... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Q46E (page 281)

In Table 7.5, the pattern that develops with increasing n suggests that the number of different sets ofl,mlvalues for a given energy level n isn2. Prove this mathematically by summing the allowed values ofmlfor a givenlover the allowed values oflfor a given n.

Short Answer

Expert verified

The number of different sets ofl,ml values for a given energy level n isn2 .

Step by step solution

01

 Given data

Energy level = n.

02

 Approach to find the final answer

For each n that is the principal quantum number, l, which is the azimuthal quantum number, can be from 0 to n 鈥� 1; for each n, there are 2l+1 allowed values ofml.

03

 To prove the number of different sets of l,ml values for a given energy level n is n2

Summing all the allowed values ofml for a given l over the allowed values of l for a given n as:

鈭�0n-12l+1=20+n-12n+n=n-1n+n=n2-n+n=n2

Thus, the number of different sets ofl,ml values for a given energy level n isn2 .

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

For a hydrogen atom in the ground state. determine (a) the most probable location at which to find the electron and (b) the most probable radius at which to find the electron, (c) Comment on the relationship between your answers in parts (a) and (b).

What are the dimensions of the spherical harmonics 螛l,ml(胃)桅ml(蠒)given in Table 7.3? What are the dimensions of theRn,l(r)given in Table 7.4, and why? What are the dimensions ofP(r), and why?

Consider two particles that experience a mutual force but no external forces. The classical equation of motion for particle 1 is v藱1=F2on1/m1, and for particle 2 is v藱2=F1on2/m2, where the dot means a time derivative. Show that these are equivalent to v藱cm=constant, and v藱rel=FMutual/渭 .Where, v藱cm=(m1v藱1+m2v藱2)/(m1m2),FMutual=-Fion2and渭=m1m2(m1+m2).

In other words, the motion can be analyzed into two pieces the center of mass motion, at constant velocity and the relative motion, but in terms of a one-particle equation where that particle experiences the mutual force and has the 鈥渞educed mass鈥� 渭.

Consider an electron in the ground state of a hydrogen atom. (a) Sketch plots of E and U(r) on the same axes (b) Show that, classically, an electron with this energy should not be able to get farther than 2a0from the proton. (c) What is the probability of the electron being found in the classically forbidden region?

A mathematical solution of the azimuthal equation (7-22) is 桅(蠁)=Ae-顿蠁+Be-顿蠁 , which applies when D is negative, (a) Show that this simply cannot meet itself smoothly when it finishes a round trip about the z-axis. The simplest approach is to consider 蠁=0 and 蠁=2蟺. (b) If D were 0, equation (7-22) would say simply that the second derivative 桅(蠁)of is 0. Argue than this too leads to physically unacceptable solution, except in the special case of 桅(蠁) being constant, which is covered by the ml=0 , case of solutions (7-24).
See all solutions

Recommended explanations on Physics Textbooks

Astrophysics

Read Explanation

Torque and Rotational Motion

Read Explanation

Nuclear Physics

Read Explanation

Waves Physics

Read Explanation

Circular Motion and Gravitation

Read Explanation

Physics of Motion

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.