Concept explainers
(a)
The longest wavelength corresponding to a transition of photon’s energy.
(a)
Answer to Problem 6P
The longest wavelength corresponding to a transition of photon’s energy is
Explanation of Solution
The longest wavelength of the photon implies lowest frequency and smallest energy. The electron makes a transition from
Write the expression for energy emitted by the electron in a transition from
Here,
Conclusion:
The energy emitted by the electron in a transition from
Therefore, the longest wavelength corresponding to a transition of photon’s energy is
(b)
The longest wavelength of the corresponding transition.
(b)
Answer to Problem 6P
The longest wavelength of the corresponding transition is
Explanation of Solution
Write the expression from the relation between frequency and wavelength.
Here,
Write the expression for photon’s energy.
Here,
Rewrite the equation (II) for frequency.
Conclusion:
Substitute equation (III) in equation (I).
Substitute
This is the red Balmer alpha line, which gives its characteristic color to the chromospheres of the sun and to photograph of the Orion nebula.
Therefore, the longest wavelength of the corresponding transition is
(c)
The shortest wavelength corresponding to a transition of photon’s energy.
(c)
Answer to Problem 6P
The shortest wavelength corresponding to a transition of photon’s energy is
Explanation of Solution
The shortest wavelength of the photon implies highest frequency and greatest energy. The electron makes a transition from
Write the expression for energy emitted by the electron in a transition from
Here,
Conclusion:
The energy emitted by the electron in a transition from
Therefore, the shortest wavelength corresponding to a transition of photon’s energy is
(d)
The shortest wavelength of the corresponding transition.
(d)
Answer to Problem 6P
The shortest wavelength of the corresponding transition is
Explanation of Solution
Write the expression from the relation between frequency and wavelength.
Here,
Write the expression for photon’s energy.
Here,
Rewrite the equation (II) for frequency.
Conclusion:
Substitute equation (III) in equation (I).
Substitute
Therefore, the smallest wavelength of the corresponding transition is
(e)
The shortest possible wavelength in the Balmer series.
(e)
Answer to Problem 6P
The shortest possible wavelength in the Balmer series is
Explanation of Solution
The transition limit in Balmer series is from
Conclusion:
Therefore, the shortest possible wavelength in the Balmer series is
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Chapter 29 Solutions
Principles of Physics: A Calculus-Based Text
- A visible (violet) emission spectral line for chromium (Cr) occurs at wavelength λ = 425.435 nm. A) What is the frequency (ν) of this light?(Give correct units and answer to six significant figures.) B) What is the magnitude of the energy change associated with the emission of one mole of photons of light with this wavelength?arrow_forwardA sodium atom in one of the states labeled “Lowest excited levels” in Fig. remains in that state, on average, for 1.6 * 10-8 s before it makes a transition to the ground state, emitting a photon with wavelength 589.0 nm and energy 2.105 eV. What is the uncertainty in energy of that excited state? What is the wavelength spread of the corresponding spectral line?arrow_forwardFor a hydrogen-like atom (the atom contains only one electron, like singly ionized He, doubly ionized Lithium, etc.), the energy levels are given by En = -Z2(13.6)/n2 eV where Z is the atomic number. If an electron in a doubly ionized Lithium atom jumps from the 2nd excited state to the ground state, what would be the wavelength of the emitted photon? A) 3.21 nm B) 3.21 pm C) 6.42 pm D) none of these.arrow_forward
- a. The electron of a hydrogen atom is excited into a higher energy level from a lower energy level. A short time later the electron relaxes down to the no = 1 energy level, releasing a photon with a wavelength of 93.83 nm. Compute the quantum number of the energy level the electron relaxes from, nhi. Note: the Rydberg constant in units of wavenumbers is 109,625 cm-1 nhi =16 b. What would the wavenumber, wavelength and energy of the photon be if instead no = 1 and nhi = 4? V: 6.9121e14 x (cm-¹) λ: (nm) E: 45.8e-20 ✓ (1)arrow_forwardIn designing an experiment, you want a beam of photons and a beam of electrons with the same wavelength of 0.281 nm, equal to the separation of the Na and Cl ions in a crystal of NaCl. Find the energy of the photons and the kinetic energy of the electrons in electro Volts (eV).arrow_forwardThe energy levels of the Bohr model for the atom can be expressed mathematically as En -13.6 eV, where Z is the atomic number, and n is the quantum number. This model is reasonably accurate for hydrogen and for singly ionized helium. The photon associated with the transition of an electron from the ground state to the first excited state in singly ionized helium has a different wavelength than that associated with a similar transition in hydrogen. Which of the following correctly describes the wavelengths of these two photons in terms of the energy level diagrams for hydrogen and helium? The photon absorbed by hydrogen has a longer wavelength than that absorbed by helium, because the energy levels in the diagram for hydrogen are more closely spaced than in the diagram for helium. B The photon absorbed by hydrogen has a shorter wavelength than that absorbed by helium, because the energy levels in the diagram for hydrogen are more closely spaced than in the diagram for helium. The photon…arrow_forward
- A sodium atom makes a transition from the first excited state to the groundstate, emitting a 589.0-nm photon with energy 2.105 eV. If the lifetime of this excited state is 1.6 × 10−8 s , what is the uncertainty in energy of this excited state? What is the width of the corresponding spectral line?arrow_forwardQuestion 9. While most transition metals have work functions corresponding to photon frequencies that are larger (higher) than visible light, alkali and alkaline earth metals have low-energy work functions. For example, calcium has a work function of o = 4.3419×10-19 J. (a) What is the initial state n, for the hydrogen emission lines at visible wavelengths (i.e., those with n = 2) for the lowest-energy photon that would eject an electron from calcium? %3! (b) If the colors of the visible hydrogen emission lines (n; = 3 to n = 6) are red, green, blue and %3D violet, which colors are capable of ejecting the electrons from calcium? (c) The energy of the emitted photon you identified in part (a), is not identical to the workfunction of calcium. Therefore, the electron is ejected from the metal surface with some kinetic energy (i.e., energy is conserved in the photoelectric effect process). What would the velocity of the electron ejected from calcium (in meters per second)?arrow_forwardConsider the electron of a Li2+ ion that undergoes a transition from a higher energy state n to its adjacent lower energy state n – 1 (e.g. n = 2→1, 3→2, 4→3, etc) and emits a photon. Suppose the emitted photon is used to strike the surface of potassium, which has a threshold frequency of 5.464 × 10^14 s–1. What is the maximum initial quantum number, n, that is required in order to emit a photon with high enough energy to generate a photocurrent from the metal surface?arrow_forward
- The Balmer series for the hydrogen atom corresponds to electronic transitions that terminate in the state with quantum number n = 2 as shown in the figure below. Consider the photon of longest wavelength corresponding to a transition shown in the figure. (a) Determine its energy. eV (b) Determine its wavelength. nm Consider the spectral line of shortest wavelength corresponding to a transition shown in the figure. (c) Find its photon energy. eV (d) Find its wavelength. nm (e) What is the shortest possible wavelength in the Balmer series? (Be sure to consider all values of n, not just those indicated by the arrows in the figure.) nmarrow_forwardA visible (violet) emission spectral line for chromium (Cr) occurs at wavelength λ = 425.435 nm.What is the frequency (ν) of this light?(Mind the units carefully. Give your answers to six significant figures.)What is the magnitude of the energy change associated with the emission of one mole of photons of light with this wavelength?arrow_forwardWhen a hydrogen atom undergoes a transition from n=3 to n=2 level, a photon with λ=656.5 nm is emitted. (a) If we imagine the atom as an electron in a one-dimensional box, what is the width of the box so that the transition from n=3 to n=2 corresponds to the emission of a photon of this wavelength? (b) For a box with the width calculated in (a), what is the ground energy state? (c) Do you think a one-dimensional box is a good model for a hydrogen atom? Because?arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningModern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage Learning