Chapter 4: Q36E (page 136)

An electron moves along the x-axiswith 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.

Short Answer

Expert verified

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

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

Step by step solution

Given.

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

Concept Introduction

The equation of an electromagnetic wave can be expressed as,

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

Calculate the value of k

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

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

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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An electron moves along the x-axiswith 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.

Short Answer

Step by step solution

Given.

Concept Introduction

Calculate the value of k

Calculate the value of ω

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Most popular questions from this chapter

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An electron moves along the x-axiswith a well-defined momentum of5×10-25kg.ms. Write an expression describing the matter wave associated with this electron. Include numerical values where appropriate.

Short Answer

Step by step solution

Given.

Concept Introduction

Calculate the value of k

Calculate the value of ω

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Circular Motion and Gravitation

Linear Momentum

Electromagnetism

Oscillations

Waves Physics

Fundamentals of Physics

Study anywhere. Anytime. Across all devices.

An electron moves along the x-axiswith 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.