Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 28: Problem 1

What is the de Broglie wavelength of a basketball of mass \(0.50 \mathrm{kg}\) when it is moving at \(10 \mathrm{m} / \mathrm{s} ?\) Why don't we see diffraction effects when a basketball passes through the circular aperture of the hoop?

Short Answer

Expert verified
Answer: The diffraction effects become noticeable when the size of the aperture (i.e., the hoop) is comparable to the de Broglie wavelength of the particle. In this case, the de Broglie wavelength of the basketball is \(1.33 \times 10^{-34}\,\mathrm{m}\), while the diameter of a standard basketball hoop is \(0.46\,\mathrm{m}\). The wavelength of the basketball is many orders of magnitude smaller than the diameter of the hoop, which means the diffraction effects are negligible and not noticeable when the basketball passes through the hoop.

Step by step solution

01

Understanding de Broglie's wavelength formula

The de Broglie wavelength is determined by the following formula: $$ \lambda = \frac{h}{mv} $$ where \(\lambda\) is the de Broglie wavelength, \(h\) is the Planck's constant (\(6.626 \times 10^{-34} \mathrm{J} \cdot \mathrm{s}\)), \(m\) is the mass of the particle, and \(v\) is the velocity of the particle.
02

Calculating the wavelength of the basketball

We are given the mass \(m = 0.50\,\mathrm{kg}\) and the velocity \(v = 10\,\mathrm{m/s}\) of the basketball. We now use the de Broglie's wavelength formula to calculate the wavelength : $$ \lambda = \frac{h}{mv} $$ $$ \lambda = \frac{6.626 \times 10^{-34}\, \mathrm{J} \cdot \mathrm{s}}{(0.50\, \mathrm{kg})(10\, \mathrm{m/s})} $$ $$ \lambda \approx 1.33 \times 10^{-34}\, \mathrm{m} $$
03

Understanding why diffraction effects aren't seen with the basketball

The diffraction effects become noticeable when the size of the aperture (i.e., the hoop) is comparable to the wavelength of the particle. The diameter of a standard basketball hoop is \(0.46\,\mathrm{m}\), while the de Broglie wavelength of the basketball is \(1.33 \times 10^{-34}\,\mathrm{m}\). We can see that the wavelength is many orders of magnitude smaller than the diameter of the hoop. Consequently, the diffraction effects are negligible and not noticeable when the basketball passes through the hoop.

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 ground-state electron configuration of bromine (Br, atomic number 35)?
An electron is confined to a one-dimensional box of length \(L\). When the electron makes a transition from its first excited state to the ground state, it emits a photon of energy 0.20 eV. (a) What is the ground-state energy (in electron-volts) of the electron in this box? (b) What are the energies (in electron-volts) of the photons that can be emitted when the electron starts in its third excited state and makes transitions downwards to the ground state (either directly or through intervening states)? (c) Sketch the wave function of the electron in the third excited state. (d) If the box were somehow made longer, how would the electron's new energy level spacings compare with its old ones? (Would they be greater, smaller, or the same? Or is more information needed to answer this question? Explain.)
(a) What are the electron configurations of the ground states of lithium \((Z=3),\) sodium \((Z=11),\) and potassium \((Z=19) ?\) (b) Why are these elements placed in the same column of the periodic table?
What are the possible values of \(L_{z}\) (the component of angular momentum along the \(z\) -axis) for the electron in the second excited state \((n=3)\) of the hydrogen atom?
A beam of neutrons is used to study molecular structure through a series of diffraction experiments. A beam of neutrons with a wide range of de Broglie wavelengths comes from the core of a nuclear reactor. In a time-offlight technique, used to select neutrons with a small range of de Broglie wavelengths, a pulse of neutrons is allowed to escape from the reactor by opening a shutter very briefly. At a distance of \(16.4 \mathrm{m}\) downstream, a second shutter is opened very briefly 13.0 ms after the first shutter. (a) What is the speed of the neutrons selected? (b) What is the de Broglie wavelength of the neutrons? (c) If each shutter is open for 0.45 ms, estimate the range of de Broglie wavelengths selected.
See all solutions

Recommended explanations on Physics Textbooks

Fields in Physics

Read Explanation

Kinematics Physics

Read Explanation

Magnetism

Read Explanation

Nuclear Physics

Read Explanation

Engineering Physics

Read Explanation

Magnetism and Electromagnetic Induction

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