Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 6: Problem 52

Can the de Broglie wavelength of a particle be known exactly?

Short Answer

Expert verified
No, the de Broglie wavelength of a particle cannot be known exactly due to the Heisenberg Uncertainty Principle, which states that the exact position and momentum of a particle cannot be simultaneously known.

Step by step solution

01

Understanding Wave-Particle Duality

In 1924, Louis de Broglie proposed that particles of matter, not just light, also have a wave-like nature. This concept, known as wave-particle duality, suggests that all matter exhibits both particle and wave characteristics. The wavelength associated with any particle is known as the de Broglie wavelength, given by the relation \(\lambda = \frac{h}{p}\), where \(\lambda\) is the de Broglie wavelength, \(h\) is the Planck's constant, and \(p\) is the momentum of the particle.
02

Understanding Heisenberg Uncertainty Principle

The Heisenberg Uncertainty Principle states that it's impossible to simultaneously know the exact position and momentum of a particle. Mathematically, it can be expressed as \(\Delta x \cdot \Delta p \geq \frac{h}{4\pi}\), where \(\Delta x\) is the uncertainty in position and \(\Delta p\) is the uncertainty in momentum.
03

Apply Uncertainty Principle to de Broglie's hypothesis

Given that the de Broglie wavelength of a particle is directly related to its momentum (through de Broglie's equation), the Heisenberg Uncertainty Principle tells us that we cannot know both the exact position and momentum of a particle simultaneously. Thus, we cannot know the exact value of a particle's de Broglie wavelength at the same time as its exact position.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

What is the frequency of the photon absorbed when the hydrogen atom makes the transition from the ground state to the \(n=4\) state?

A triply ionized atom of beryllium \(\mathrm{Be}^{3+}\) is a hydrogen-like ion. When \(\mathrm{Be}^{3+}\) is in one of its excited states, its radius in this \(n\) th state is exactly the same as the radius of the first Bohr orbit of hydrogen. Find \(n\) and compute the ionization energy for this state of \(\mathrm{Be}^{3+}\).

The cutoff wavelength for the emission of 7. photoelectrons from a particular surface is \(500 \mathrm{nm}\). Find the maximum kinetic energy of the ejected photoelectrons when the surface is illuminated with light of wavelength \(600 \mathrm{nm}\).

Find the Lorentz factor \(\gamma\) and de Broglie's wavelength for a 1.0 -TeV proton in a particle accelerator.

What is the wavelength of (a) a 12 -keV X-ray photon; (b) a 2.0 -MeV \(\gamma\) -ray photon?
See all solutions

Recommended explanations on Physics Textbooks

Fluids

Read Explanation

Electricity

Read Explanation

Oscillations

Read Explanation

Wave Optics

Read Explanation

Dynamics

Read Explanation

Translational Dynamics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free