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Introductory Chemistry: A Foundati...

9th Edition
Steven S. Zumdahl + 1 other
ISBN: 9781337399425

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BuyFindarrow_forward

Introductory Chemistry: A Foundati...

9th Edition
Steven S. Zumdahl + 1 other
ISBN: 9781337399425
Textbook Problem
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n the text (Section 11.6) it was mentioned that current theories of atomic structure suggest that all matter and all energy demonstrate both particle-like and wave—like properties under the appropriate conditions, although the wavelike nature of matter becomes apparent only in very small and very fast-moving particles. The relationship between wavelength ( λ ) observed for a particle and the mass and velocity of that particle is called the de Broglie relationship. It is.

>     λ = h l m v

which h is Planck‘s constant ( 6 . 63  ×  l 0 34 .  s ) , × m represents the mass of the particle in kilograms, and v represents the velocity of the particle in meters per second. Calculate the “de Broglie wavelength" for each of the following, and use your numerical answers to explain why macroscopic (large) objects are not ordinarily discussed in terms of their “wave-like” properties.

>a. an electron moving at 0. 9 0 times the speed of light

>b. a 15 0 g ball moving at a speed of 1 0  m / s

a 75 kg person walking at a speed of 2 .0  km / h

Interpretation Introduction

(a)

Interpretation:

The de-Broglie wavelength is to be calculated.

Concept Introduction:

In 1924, de-Broglie suggested the dual nature of microscopic particles and compared the energy value of both particle and wave nature particles. According to him, the wavelength of an electron (λ) moving with a speed of v is:

λ=hmv

Where,

  • h is Plank’s constant.
  • m is the mass of electron.
Explanation

Mass of electron =9.10×1031kg

Speed of light =3×108ms1

Given: The speed of electron is 0.9 times the speed of light.

So the speed of electron, v=0.9×3×108ms-1

The formula for the calculation of de-Broglie wavelength is:

λ=hmv

The value of Plank’s constant, h=6

Interpretation Introduction

(b)

Interpretation:

The de-Broglie wavelength is to be calculated and the reason as to why macroscopic particles cannot be treated as wave particle is to be stated.

Concept Introduction:

In 1924, de-Broglie suggested the dual nature of microscopic particles and compared the energy value of both particle and wave nature particles. According to him, the wavelength of an electron (λ) moving with a speed of v is:

λ=hmv

Where,

  • h is Plank’s constant.
  • m is the mass of electron.
Interpretation Introduction

(b)

Interpretation:

The de-Broglie wavelength is to be calculated and the reason as to why macroscopic particles cannot be treated as wave particle is to be stated.

Concept Introduction:

In 1924, de-Broglie suggested the dual nature of microscopic particles and compared the energy value of both particle and wave nature particles. According to him, the wavelength of an electron (λ) moving with a speed of v is:

λ=hmv

Where,

  • h is Plank’s constant.
  • m is the mass of electron.
Interpretation Introduction

(c)

Interpretation:

The de-Broglie wavelength is to be calculated and the reason as to why macroscopic particles cannot be treated as wave particle is to be stated.

Concept Introduction:

In 1924, de-Broglie suggested the dual nature of microscopic particles and compared the energy value of both particle and wave nature particles. According to him, the wavelength of an electron (λ) moving with a speed of v is:

λ=hmv

Where,

  • h is Plank’s constant.
  • m is the mass of electron.

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