BuyFindarrow_forward

College Physics

1st Edition
Paul Peter Urone + 1 other
ISBN: 9781938168000

Solutions

Chapter
Section
BuyFindarrow_forward

College Physics

1st Edition
Paul Peter Urone + 1 other
ISBN: 9781938168000
Textbook Problem

Verify Equations r n = n 2 Z a B and a B = h 2 4 π 2 m e k q e 2 = 0.529 × 10 10 m using the approach stated in the text. That is, equate the Coulomb and centripetal forces and then insert an expression for velocity from the condition for angular momentum quantization.

To determine

To prove:

The equation:rn=n2/Z(aB) , whereaB=h2/4Π2mekqe2=0.529×1010 m.

Explanation

Given info:

Equate the coulomb and centripetal forces and insert the value for the velocity from the condition of quantization of angular momentum.

Formula used:

For Coulombs force:kZqe2/rn2

For Centripetal force:mev2/rn

The equationrn=n2/Z(aB) andaB=h2/4Π2mekqe2 are used to calculate the radii of allowed (quantized) electron orbits in the hydrogen like atoms. For example: for Hydrogen, Z= 1, r1 =aB.

Here,aB=h2/4Π2mekqe2 is called the 'Bohr Radius'.

Proof:

Equating the equations for coulomb interaction and centripetal force together, we get:

kqe2/rn2=mev2/rnrn=kZqe2/mev2rn=kZqe2/me(1/v2)

From:mevrn=n(h/2Π) (Quantization of angular momentum)

rn=(kZqe2/me)×(4Π2me<

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Additional Science Solutions

Find more solutions based on key concepts

Show solutions add

After circulating around the cells of the tissues, all extracellular fluid then a. evaporates from the body. b....

Nutrition: Concepts and Controversies - Standalone book (MindTap Course List)

How does hydrostatic equilibrium relate to hot-air ballooning?

Horizons: Exploring the Universe (MindTap Course List)

What is physically exchanged during crossing over?

Human Heredity: Principles and Issues (MindTap Course List)

What is a life cycle?

Biology: The Dynamic Science (MindTap Course List)

A 3-kg object moving to the right on a frictionless, horizontal surface with a speed of 2 m/s collides head-on ...

Physics for Scientists and Engineers, Technology Update (No access codes included)