Domanda del libro di testo
Draw an energy-level diagram, similar to Figure 38.21, for the He+ ion. On your diagram: Show the first five energy levels. Label each with the values of n and En.
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Ch 38: Quantization
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
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TOC.tableOfContents
- Ch 01: Concepts of Motion35
- Ch 02: Kinematics in One Dimension75
- Ch 03: Vectors and Coordinate Systems58
- Ch 04: Kinematics in Two Dimensions60
- Ch 05: Force and Motion23
- Ch 06: Dynamics I: Motion Along a Line53
- Ch 07: Newton's Third Law27
- Ch 08: Dynamics II: Motion in a Plane52
- Ch 09: Work and Kinetic Energy56
- Ch 10: Interactions and Potential Energy50
- Ch 11: Impulse and Momentum56
- Ch 12: Rotation of a Rigid Body71
- Ch 13: Newton's Theory of Gravity52
- Ch 14: Fluids and Elasticity44
- Ch 15: Oscillations55
- Ch 16: Traveling Waves37
- Ch 17: Superposition39
- Ch 18: A Macroscopic Description of Matter53
- Ch 19: Work, Heat, and the First Law of Thermodynamics60
- Ch 20: The Micro/Macro Connection53
- Ch 21: Heat Engines and Refrigerators34
- Ch 22: Electric Charges and Forces40
- Ch 23: The Electric Field39
- Ch 24: Gauss' Law32
- Ch 25: The Electric Potential63
- Ch 26: Potential and Field57
- Ch 27: Current and Resistance42
- Ch 28: Fundamentals of Circuits39
- Ch 29: The Magnetic Field47
- Ch 30: Electromagnetic Induction60
- Ch 31: Electromagnetic Fields and Waves32
- Ch 32: AC Circuits63
- Ch 33: Wave Optics32
- Ch 34: Ray Optics57
- Ch 35: Optical Instruments30
- Ch 36: Special Relativity38
- Ch 37: The Foundations of Modern Physics25
- Ch 38: Quantization49
- Ch 39: Wave Functions and Uncertainty31
- Ch 40: One-Dimensional Quantum Mechanics35
- Ch 41: Atomic Physics18
- Ch 42: Nuclear Physics27
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Non è quello che usi tu?Cambia libro di testo
Capitolo 38, Problema 61a
What wavelength photon does a hydrogen atom emit in a 200→199 transition?
Guida verificata passo dopo passo1
Step 1: Understand the problem. The hydrogen atom emits a photon when transitioning from a higher energy level (n=200) to a lower energy level (n=199). The energy difference between these levels determines the wavelength of the emitted photon.
Step 2: Use the Rydberg formula to calculate the energy difference between the two levels. The formula for the energy of a hydrogen atom's electron in a given energy level is: , where R H h 2 n is the principal quantum number.
Step 3: Calculate the energy difference between the two levels using the formula: . Substitute the values of n = 200 and n = 199 into the energy formula to find the energy difference.
Step 4: Relate the energy difference to the wavelength of the emitted photon using the equation: , where h is Planck's constant, c is the speed of light, and ΔE is the energy difference calculated in Step 3.
Step 5: Substitute the known constants (h , c , and R H
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Photon Emission
Photon emission occurs when an electron in an atom transitions from a higher energy level to a lower one, releasing energy in the form of a photon. The energy of the emitted photon corresponds to the difference in energy between the two levels, which can be calculated using the formula E = hf, where E is energy, h is Planck's constant, and f is the frequency of the photon.
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13:08
Radiation
Energy Levels in Hydrogen Atom
In a hydrogen atom, electrons occupy discrete energy levels, which are quantized. The energy levels can be described by the formula E_n = -13.6 eV/n², where n is the principal quantum number. The transition from one level to another, such as from n=200 to n=199, results in the emission of a photon with a specific wavelength determined by the energy difference between these levels.
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01:06Charge of Atom
Wavelength Calculation
The wavelength of a photon can be calculated using the relationship between energy and wavelength given by the equation λ = hc/E, where λ is the wavelength, h is Planck's constant, c is the speed of light, and E is the energy of the photon. By determining the energy difference for the transition and applying this formula, one can find the wavelength of the emitted photon.
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05:42Unknown Wavelength of Laser through Double Slit
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Domanda del libro di testo
Consider a hydrogen atom in stationary state n. On average, an atom stays in the n = 2 state for 1.6 ns before undergoing a transition to the n = 1 state. On average, how many revolutions does the electron make before the transition?
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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?
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Domanda del libro di testo
What is the difference in the wavelengths emitted in a 199→2 transition and a 200→2 transition?
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Domanda del libro di testo
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.
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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.
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