Book edition 2nd Edition

Author(s) Randy Harris

Pages 633 pages

ISBN 9780805303087

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Short Answer

An electron moves along the x-axis with a well-defined momentum of $5 \times 10^{- 25} k g . \frac{m}{s}$ . Write an expression describing the matter wave associated with this electron. Include numerical values where appropriate.

A statement that describes the matter wave that this electron is linked with

$ψ (x, t) = A e x p ((7.54 \times 10^{8} m^{- 1}) x - (2.07 \times 10^{15} a^{- 1}) t)$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given.

The momentum of the electron is $p = 5 \times 10^{- 25} k g \cdot m / s$

Step 2: Concept Introduction

The equation of an electromagnetic wave can be expressed as,

$ψ (x, t) = A e^{i (k x - ω t)}$ …………(1)

Step 3: Calculate the value of k

As a result, we must determine the values of k and w .

$\begin{array}{rcl} p & = & h k \\ k & = & \frac{p}{h} \\ k & = & \frac{5 \times 10^{- 25} k g \cdot m / s}{6.63 \times 10^{- 34} k g \cdot m^{2} / s} \\ k & = & 7.54 \times 10^{8} m^{- 1} \dots \dots \dots \dots \dots \dots . . (2) \end{array}$

Step 3: Calculate the value of ω

$E = h ω ω = \frac{E}{h} ω = \frac{\frac{p^{2}}{2 m}}{h} ω = \frac{p^{2}}{2mh}$

$\begin{array}{rcl} ω & = & \frac{p^{2}}{2mh} \\ = & \frac{25 \times 10^{- 50} k g^{2} . \frac{m^{2}}{s^{2}}}{2 \times (9.1 \times 10^{- 31} kg) \times (6.63 \times 10^{- 34} k g . \frac{m}{s})} \end{array}$

$ω = 2.07 \times 10^{15} s^{- 1} . . . . . . . . . . . . . . (1)$

Substitute values from equations (2) and (3) into equation (1), and we get,

$ψ (x, t) = A e x p ((7.54 \times 10^{8} m^{- 1}) x - (2.07 \times 10^{15} s^{- 1}) t)$ .

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Modern Physics

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Short Answer

An electron moves along the x-axis with a well-defined momentum of $5 \times 10^{- 25} k g . \frac{m}{s}$ . Write an expression describing the matter wave associated with this electron. Include numerical values where appropriate.

Step by Step Solution

Step 1: Given.

Step 2: Concept Introduction

Step 3: Calculate the value of k

Step 3: Calculate the value of ω

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Modern Physics

Answers without the blur.

Short Answer

An electron moves along the x-axis with a well-defined momentum of 5×10-25kg.ms. Write an expression describing the matter wave associated with this electron. Include numerical values where appropriate.

Step by Step Solution

Step 1: Given.

Step 2: Concept Introduction

Step 3: Calculate the value of k

Step 3: Calculate the value of ω

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An electron moves along the x-axis with a well-defined momentum of $5 \times 10^{- 25} k g . \frac{m}{s}$ . Write an expression describing the matter wave associated with this electron. Include numerical values where appropriate.