When 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

When 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

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter28: Quantum Physics

Section: Chapter Questions

Problem 73P

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When an electron in a one-dimensional box makes a transition from the n = 1 energy level to the n = 2 level, it absorbs a photon of wavelength 426 nm. What is the wavelength of that photon when the electron undergoes a transition (a) from the n = 2 to the n = 3 energy level and (b) from the n = 1 to the n = 3 energy level? (c) What is the width L of the box?
A 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?
(a) An atom initially in an energy level with E = -6.52 eV absorbs a photon that has wavelength 860 nm. What is the internal energy of the atom after it absorbs the photon? (b) An atom initially in an energy level with E = -2.68 eV emits a photon that has wave- length 420 nm. What is the internal energy of the atom after it emits the photon?
An atom in an excited state of 4.7 eV emits a photon and ends up in the ground state. The lifetime of the excited state is 1.0 x 10-13 s. (a) What is the energy uncertainty of the emitted photon? (b) What is the spectral line width (in wavelength) of the photon?
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?
(a) An atom initially in an energy level with E = -6.52 eV absorbs a photon that has wavelength 860 nm. What is the internal energy of the atom after it absorbs the photon? (b) An atom initially in an energy level with E = -2.68 eV emits a photon that has wavelength 420 nm. What is the internal energy of the atom after it emits the photon?
For 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.
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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?
a)Suppose a hydrogen molecule in its ground state is dissociated by absorbing a photon of ultraviolet light, causing the two hydrogen atoms to fly apart. What photon energy will give each atom a speed of 19 km/s? The mass of a hydrogen atom is 1.7×10^−27 kg Express your answer to two significant figures and include the appropriate units.
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