Ch 38: Quantization

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Non è quello che usi tu?Cambia libro di testo

Knight Calc 5th Edition

Ch 38: Quantization

Problema 19a

Capitolo 38, Problema 19a

What is the de Broglie wavelength of a 200 g baseball with a speed of 30 m/s?

Guida verificata passo dopo passo

Step 1: Recall the formula for the de Broglie wavelength, which is given by \( \lambda = \frac{h}{p} \), where \( \lambda \) is the wavelength, \( h \) is Planck's constant \( (6.626 \times 10^{-34} \, \text{J·s}) \), and \( p \) is the momentum of the object.

Step 2: Calculate the momentum \( p \) of the baseball using the formula \( p = m \cdot v \), where \( m \) is the mass of the baseball (200 g converted to kilograms, \( 0.2 \; \text{kg} \)) and \( v \) is its velocity (30 m/s).

Step 3: Substitute the values of \( m \) and \( v \) into the momentum formula to find \( p \). This gives \( p = 0.2 \cdot 30 \; \text{kg·m/s} \).

Step 4: Substitute the calculated momentum \( p \) into the de Broglie wavelength formula \( \lambda = \frac{h}{p} \). Use \( h = 6.626 \times 10^{-34} \; \text{J·s} \).

Step 5: Simplify the expression to find the de Broglie wavelength \( \lambda \). Note that the result will be extremely small due to the large mass and velocity of the baseball.

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

de Broglie Wavelength

The de Broglie wavelength is a concept in quantum mechanics that describes the wave-like behavior of particles. It is given by the formula λ = h/p, where λ is the wavelength, h is Planck's constant (6.626 x 10^-34 Js), and p is the momentum of the particle. This concept illustrates that all matter exhibits both particle and wave characteristics, especially at the quantum scale.

Video consigliato:

Percorso guidato

05:42

Unknown Wavelength of Laser through Double Slit

Momentum

Momentum is a physical quantity defined as the product of an object's mass and its velocity, expressed as p = mv. In this context, the momentum of the baseball can be calculated using its mass (200 g or 0.2 kg) and its speed (30 m/s). Understanding momentum is crucial for calculating the de Broglie wavelength, as it directly influences the wave properties of the object.

Video consigliato:

Percorso guidato

05:17

Intro to Momentum

Planck's Constant

Planck's constant is a fundamental constant in quantum mechanics, denoted as h, with a value of approximately 6.626 x 10^-34 Js. It relates the energy of a photon to its frequency and plays a critical role in the formulation of the de Broglie wavelength. This constant is essential for understanding the scale at which quantum effects become significant, particularly for small particles.

Video consigliato:

Percorso guidato

08:59

Phase Constant of a Wave Function

Pratica correlata

Domanda del libro di testo

At what speed is an electron’s de Broglie wavelength (a) 1.0 nm, (b) 1.0 μm, and (c) 1.0 mm?

views

Domanda del libro di testo

INT Through what potential difference must an electron be accelerated from rest to have a de Broglie wavelength of 500 nm?

views

Domanda del libro di testo

The diameter of the nucleus is about 10 fm. What is the kinetic energy, in MeV, of a proton with a de Broglie wavelength of 10 fm?

views

Domanda del libro di testo

The diameter of the nucleus is about 10 fm. A simple model of the nucleus is that protons and neutrons are confined within a one-dimensional box of length 10 fm. What are the first three energy levels, in MeV, for a proton in such a box?

views

Domanda del libro di testo

55 keV x-ray photons are incident on a target. At what scattering angle do the scattered photons have an energy of 50 keV?

views

Domanda del libro di testo

What is the quantum number of an electron confined in a 3.0-nm-long one-dimensional box if the electron’s de Broglie wavelength is 1.0 nm?

views