Principles of Modern Chemistry
Principles of Modern Chemistry
8th Edition
ISBN: 9781305079113
Author: David W. Oxtoby, H. Pat Gillis, Laurie J. Butler
Publisher: Cengage Learning
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Chapter 4, Problem 42P

(a)

Interpretation Introduction

Interpretation:

The wave function for a highly excited state ψ100,100(x,y) for a particle in square box should be written and nodal lines number should be determined along with the number of local probability maxima for this state.

Concept introduction:

The function which describes the position of an electron and quantum state of an isolated quantum system is known as wave function.

The general formula of the wave function for a particle in a square box is:

  ψnxny(x,y)=2Lsin(nxπxL)sin(nyπyL)

Where, ψnxny(x,y) is wave function and nx,ny have values 1, 2, 3 etc.

L = length of the box.

The nodes that lie along straight lines are known as nodal lines. The points in space around the nucleus where the probability of finding electron is zero is known as nodes.

(b)

Interpretation Introduction

Interpretation:

The motion of particle should be described in this state.

Concept introduction:

The function which describes the position of an electron and quantum state of an isolated quantum system is known as wave function.

The general formula of the wave function for a particle in a square box is:

  ψnxny(x,y)=2Lsin(nxπxL)sin(nyπyL)

Where, ψnxny(x,y) is wave function and nx,ny have values 1, 2, 3 etc.

L = length of the box.

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Chapter 4 Solutions

Principles of Modern Chemistry

Ch. 4 - Excited lithium atoms emit light strongly at a...Ch. 4 - Excited mercury atoms emit light strongly at a...Ch. 4 - Barium atoms in a flame emit light as they undergo...Ch. 4 - Potassium atoms in a flame emit light as they...Ch. 4 - The sodium D-line is actually a pair of closely...Ch. 4 - The power output of a laser is measured by its...Ch. 4 - In a FranckHertz experiment on sodium atoms, the...Ch. 4 - In a FranckHertz experiment on hydrogen atoms, the...Ch. 4 - Use the Bohr model to calculate the radius and the...Ch. 4 - He+ ions are observed in stellar atmospheres. Use...Ch. 4 - The radiation emitted in the transition from n=3...Ch. 4 - Prob. 22PCh. 4 - Prob. 23PCh. 4 - When an intense beam of green light is directed...Ch. 4 - Cesium frequently is used in photocells because...Ch. 4 - Alarm systems use the photoelectric effect. A beam...Ch. 4 - Light with a wavelength of 2.50107m falls on the...Ch. 4 - Calculate the maximum wavelength of...Ch. 4 - Prob. 29PCh. 4 - Prob. 30PCh. 4 - Calculate the de Broglie wavelength of the...Ch. 4 - Calculate the de Broglie wavelength of the...Ch. 4 - Prob. 33PCh. 4 - Prob. 34PCh. 4 - (a) The position of an electron is known to be...Ch. 4 - No object can travel faster than the speed of...Ch. 4 - (a) Using Equation 4.36, make a graph of the n=3...Ch. 4 - Using a simple particle-in-a-box model for the...Ch. 4 - Chapter 3 introduced the concept of a double bond...Ch. 4 - When metallic sodium is dissolved in liquid sodium...Ch. 4 - Prob. 41PCh. 4 - Prob. 42PCh. 4 - Prob. 43PCh. 4 - Prob. 44PCh. 4 - A piano tuner uses a tuning fork that emits sound...Ch. 4 - The distant galaxy called Cygnus A is one of the...Ch. 4 - Hot objects can emit blackbody radiation that...Ch. 4 - Compare the energy (in joules) carried by an X-ray...Ch. 4 - The maximum in Planck’s formula for the emission...Ch. 4 - Prob. 50APCh. 4 - When ultraviolet light of wavelength 131 nm...Ch. 4 - Express the speed of the electron in the Bohr...Ch. 4 - Photons are emitted in the Lyman series as...Ch. 4 - Prob. 54APCh. 4 - The energies of macroscopic objects, as well as...Ch. 4 - Prob. 56APCh. 4 - Prob. 57APCh. 4 - It has been suggested that spacecraft could be...Ch. 4 - Prob. 59APCh. 4 - The normalized wave function for a particle in a...Ch. 4 - A particle of mass m is placed in a...
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