Skip to main content
Ch 38: Photons: Light Waves Behaving as Particles
Young & Freedman Calc - University Physics 15th Edition
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoYoung & Freedman Calc 15th EditionCh 38: Photons: Light Waves Behaving as ParticlesProblema 10
Capitolo 37, Problema 10

The cathode-ray tubes that generated the picture in early color televisions were sources of x rays. If the acceleration voltage in a television tube is 15.015.0 kV, what are the shortest-wavelength x rays produced by the television?

Guida verificata passo dopo passo
1
Understand that the shortest-wavelength x-rays are produced when electrons are accelerated to their maximum energy and then suddenly stopped, converting their kinetic energy into electromagnetic radiation.
Recall the formula that relates the energy of the x-rays to their wavelength: \( E = \frac{hc}{\lambda} \), where \( E \) is the energy, \( h \) is Planck's constant \( (6.626 \times 10^{-34} \text{ J s}) \), \( c \) is the speed of light \( (3.00 \times 10^8 \text{ m/s}) \), and \( \lambda \) is the wavelength.
Convert the acceleration voltage from kilovolts to joules. Since 1 electron volt (eV) is equal to \( 1.602 \times 10^{-19} \text{ J} \), multiply the voltage by this conversion factor: \( E = 15,000 \text{ eV} \times 1.602 \times 10^{-19} \text{ J/eV} \).
Substitute the energy \( E \) into the formula \( \lambda = \frac{hc}{E} \) to find the wavelength. This will give you the shortest wavelength of the x-rays produced.
Ensure units are consistent and perform the calculation to find \( \lambda \), which will be in meters. This is the shortest wavelength of x-rays produced by the television tube.

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
4m

Concetti chiave

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

Cathode-Ray Tube

A cathode-ray tube (CRT) is a vacuum tube containing one or more electron guns and a phosphorescent screen used to display images. Electrons are accelerated and deflected by electric and magnetic fields to create images on the screen. In early color televisions, CRTs were used to generate images, and the high voltage applied to accelerate electrons could produce x-rays.
Video consigliato:
Percorso guidato
18:29
Pressure Gauges: U-Shaped Tube

X-ray Production

X-rays are produced when high-energy electrons strike a material, typically a metal target. The sudden deceleration of electrons results in the emission of x-rays, a form of electromagnetic radiation. The energy and wavelength of the x-rays depend on the acceleration voltage applied to the electrons; higher voltages produce shorter wavelengths and more energetic x-rays.
Video consigliato:
Percorso guidato
09:07
Introduction to Dot Product (Scalar Product)

Energy-Wavelength Relationship

The energy of a photon is inversely proportional to its wavelength, as described by the equation E = hc/λ, where E is the energy, h is Planck's constant, c is the speed of light, and λ is the wavelength. In the context of x-ray production, the maximum energy of the x-rays corresponds to the shortest wavelength, determined by the acceleration voltage applied to the electrons.
Video consigliato:
Percorso guidato
03:43
Relationships Between Force, Field, Energy, Potential
Pratica correlata
Domanda del libro di testo

The photoelectric work function of potassium is 2.32.3 eV. If light that has a wavelength of 190190 nm falls on potassium, find the stopping potential in volts.

1636
views
Domanda del libro di testo

A photon scatters in the backward direction (ϕ=180\(\phi\)=180°) from a free proton that is initially at rest. What must the wavelength of the incident photon be if it is to undergo a 10.0%10.0\% change in wavelength as a result of the scattering?

1262
views
Domanda del libro di testo

X rays with initial wavelength 0.06650.0665 nm undergo Compton scattering. What is the longest wavelength found in the scattered x rays? At which scattering angle is this wavelength observed?

1704
views
Domanda del libro di testo

An electron and a positron are moving toward each other and each has speed 0.500c0.500c in the lab frame. What is the kinetic energy of each particle?

1477
views
Domanda del libro di testo

The photoelectric work function of potassium is 2.32.3 eV. If light that has a wavelength of 190190 nm falls on potassium, find the kinetic energy, in electron volts, of the most energetic electrons ejected.

2054
views
Domanda del libro di testo

A photon has momentum of magnitude 8.24×10−288.24\(\times\)10^{-28} kg-m/s. What is the wavelength of this photon? In what region of the electromagnetic spectrum does it lie?

1396
views