Skip to main content
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
Tutti i libri di testoKnight Calc 5th EditionCh 38: QuantizationProblema 54b
Capitolo 38, Problema 54b

The first three energy levels of the fictitious element X are shown in FIGURE P38.54. What wavelengths are observed in the absorption spectrum of element X? Express your answers in nm.

Guida verificata passo dopo passo
1
Identify the energy levels of the fictitious element X from the given figure. Let the energy levels be denoted as E₁, E₂, and E₃, where E₁ < E₂ < E₃.
Recall that in an absorption spectrum, photons are absorbed when an electron transitions from a lower energy level to a higher energy level. The energy of the absorbed photon corresponds to the difference between the two energy levels: ΔE = E_final - E_initial.
Use the relationship between the energy of a photon and its wavelength: E = h * c / λ, where h is Planck's constant (6.626 × 10⁻³⁴ J·s), c is the speed of light (3.00 × 10⁸ m/s), and λ is the wavelength. Rearrange this equation to solve for the wavelength: λ = h * c / ΔE.
Calculate the energy differences for all possible transitions that result in absorption: ΔE₁₂ = E₂ - E₁, ΔE₁₃ = E₃ - E₁, and ΔE₂₃ = E₃ - E₂. These energy differences correspond to the absorbed photon energies.
Substitute the values of ΔE₁₂, ΔE₁₃, and ΔE₂₃ into the equation λ = h * c / ΔE to calculate the wavelengths for each transition. Convert the resulting wavelengths from meters to nanometers (1 nm = 10⁻⁹ m) to express the final answers in nm.

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.

Energy Levels

Energy levels refer to the specific energies that electrons can occupy in an atom. In quantum mechanics, these levels are quantized, meaning electrons can only exist in certain states and not in between. The difference in energy between these levels determines the wavelengths of light absorbed or emitted when electrons transition between them.
Video consigliato:
Percorso guidato
04:10
Intro to Energy & Types of Energy

Absorption Spectrum

An absorption spectrum is a spectrum of absorbed light that occurs when electrons in an atom absorb specific wavelengths of light to move from a lower energy level to a higher one. Each element has a unique absorption spectrum, which can be used to identify the element based on the specific wavelengths absorbed, corresponding to the energy differences between its quantized energy levels.
Video consigliato:
Percorso guidato
06:06
The Electromagnetic Spectrum

Wavelength and Energy Relationship

The relationship between wavelength and energy is described by the equation E = hc/λ, where E is energy, h is Planck's constant, c is the speed of light, and λ is the wavelength. This equation shows that shorter wavelengths correspond to higher energy transitions. Therefore, to find the wavelengths in the absorption spectrum, one must calculate the energy differences between the energy levels and convert these energies into wavelengths.
Video consigliato:
Percorso guidato
03:43
Relationships Between Force, Field, Energy, Potential
Pratica correlata
Domanda del libro di testo

The absorption spectrum of an atom consists of the wavelengths 200 nm, 300 nm, and 500 nm. b. What wavelengths are seen in the atom’s emission spectrum?

1667
views
Domanda del libro di testo

A muon—a subatomic particle with charge −e and a mass 207 times that of an electron—is confined in a 15-pm-long, one-dimensional box. ( 1pm=1picometer=10−12 m.) What is the wavelength, in nm, of the photon emitted in a quantum jump from n = 2 to n = 1?

68
views
Domanda del libro di testo

The first three energy levels of the fictitious element X were shown in Figure P38.54. An electron with a speed of 1.4×106 m/s collides with an atom of element X. Shortly afterward, the atom emits a photon with a wavelength of 1240 nm. What was the electron’s speed after the collision? Assume that, because the atom is much more massive than the electron, the recoil of the atom is negligible. Hint: The energy of the photon is not the energy transferred to the atom in the collision.

135
views
Domanda del libro di testo

The first three energy levels of the fictitious element X are shown in FIGURE P38.54. What is the ionization energy of element X?

48
views
Domanda del libro di testo

What wavelength photon does a hydrogen atom emit in a 200→199 transition?

39
views
Domanda del libro di testo

An electron confined in a one-dimensional box emits a 200 nm photon in a quantum jump from n = 2 to n = 1. What is the length of the box?

110
views