There is an uncertainty principle for energy and time ∆E∆t ≥ ¯h/2 . This relationship can...
There is an uncertainty principle for energy and time ∆E∆t ≥ ¯h/2 . This relationship can be applied to the excited state energies and their lifetimes of atoms and molecules.
a) Show that both sides of the expression for time-energy uncertainty relationship have the same units.
b) If the lifetime of a molecule at its excited state is 1 nanosecond, what is the uncertainty of the energy (in eV) of this state?
c) If a 10-femtosecond laser is used to probe an excited state of a molecule, what is the uncertainty in the measured energy for this laser?
d) If a molecule is in its ground state (the eigenfunction of a system’s Hamiltonian), what is the uncertainty in its energy? In time? Does your result have a physical sense? Explain.
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There is an uncertainty principle for energy and time ∆E∆t ≥
¯h/2 . This relationship can...
true/false 1. Energy of absorbed photon equals energy of emitted photon. 2. Following emission, molecule returns...
true/false 1. Energy of absorbed photon equals energy of emitted photon. 2. Following emission, molecule returns to its lowest energy state by a series of rapid vibrational relaxations. 3. The lifetime of the excited vibrational states is about a femtosecond; the lifetime of the excited electronic state is generally longer than a nanosecond. 4. Photon absorption usually occurs when a molecule is in its ground electronic state.
Artificial rubies have an atomic system consisting of three main energy levels and can be used to...
Artificial rubies have an atomic system consisting of three main energy levels and can be used to produce short pulses of laser light. The energies of these levels are Eo, E1 and E2, in increasing order of energy (a) Write down an expression giving the relative population of the energy levels Eo and E1 at thermal equilibrium. b) Explain what is meant by the term population inversion. Described how this is achieved in a three-level laser system Photons of wavelength...
Determine the uncertainty in energy of the photon using the time-energy uncertainty relationship,emitted during the following...
Determine the uncertainty in energy of the photon using the time-energy uncertainty relationship,emitted during the following atomic transitions: a) The ground state hyperfine transition in hydrogen with a lifetime of 10^6 years b) The Carbon 1s π∗ transition with a lifetime of 6.9 × 10^−15s
3 (b) The energy of a Bohr atom in the n-th excited state is given by the formula E--a2mc2 2,7, where α-e2/(4πέρ,10hc)-1 /137, m is the electron mass and e denotes the electron electric charge. i) Wh...
3 (b) The energy of a Bohr atom in the n-th excited state is given by the formula E--a2mc2 2,7, where α-e2/(4πέρ,10hc)-1 /137, m is the electron mass and e denotes the electron electric charge. i) Why is the total energy negative? Explain briefly your answer. ii) What is the radius of the electron in the n-th excited state in the Bohr atom? To answer that correctly follow the next steps Use Bohr's angular momentum quantization principle to obtain an...
Q10M.9 Consider an HCl molecule. The hydrogen atom irn this molecule has a mass we can look up (s...
Q10M.9 Consider an HCl molecule. The hydrogen atom irn this molecule has a mass we can look up (see the inside front cover), and the chlorine mass is enough larger that we can (to a first degree of approximation) consider it to be fixed. The bond between these atoms has a local minimum .13 nm, and for "small oscillations" around that minimum, the bond's potential energy can be modeled as a harmonic oscillator potential energy function. Suppose we find that...
2. This problem will help you understand how two atoms can form a molecule through the...
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5. A diatomic molecule (like H2) can be modeled as two atoms of equal mass m,...
5. A diatomic molecule (like H2) can be modeled as two atoms of equal mass m, connected by a rigid massless rod of length a. The system is free to rotate in 3-D. I claim the moment of inertia of this molecule around its ceater of mass is a. (Feel free to convince yourself that factor of k is coect!) Big hint if you 're having trouble getting started: this problem is directly related to McIntyre's Ch A) The energy...
A particle with mass m is in a one-dimensional simple harmonic oscillator potential. At time t = 0 it is described by the state where lo and l) are normalised energy eigenfunctions corresponding to e...
A particle with mass m is in a one-dimensional simple harmonic oscillator potential. At time t = 0 it is described by the state where lo and l) are normalised energy eigenfunctions corresponding to energies E and Ey and b and c are real constants. (a) Find b and c so that (x) is as large as possible. b) Write down the wavefunction of this particle at a time t later c)Caleulate (x) for the particle at time t (d)...
Question 8 please 5. We start with Schrodinger's Equation in 2(x,t) = H¥(x,t). We can write...
Question 8 please
5. We start with Schrodinger's Equation in 2(x,t) = H¥(x,t). We can write the time derivative as 2.4(x, t) = V(x,+) - (xt), where At is a sufficiently small increment of time. Plug the algebraic form of the derivative into Schrodinger's Eq. and solve for '(x,t+At). b. Put your answer in the form (x,t+At) = T '(x,t). c. What physically does the operator T do to the function '(x,t)? d. Deduce an expression for '(x,t+24t), in terms...
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I.(20p) Fill the following spaces with or circle the appropriate answers (can be more than one!). I.1. In Tom's frame of reference, two events A and B take place at different locations along the x axis but are observed by Tom to be simultaneous. Which of the following statements is true? (1) No observers moving relative to Tom will find A and B to be simultaneous, but some may see A before B and others B before A. (2) No...
Artificial rubies have an atomic system consisting of three main energy levels and can be used to produce short pulses of laser light. The energies of these levels are Eo, E1 and E2, in increasing order of energy (a) Write down an expression giving the relative population of the energy levels Eo and E1 at thermal equilibrium. b) Explain what is meant by the term population inversion. Described how this is achieved in a three-level laser system Photons of wavelength...
3 (b) The energy of a Bohr atom in the n-th excited state is given by the formula E--a2mc2 2,7, where α-e2/(4πέρ,10hc)-1 /137, m is the electron mass and e denotes the electron electric charge. i) Why is the total energy negative? Explain briefly your answer. ii) What is the radius of the electron in the n-th excited state in the Bohr atom? To answer that correctly follow the next steps Use Bohr's angular momentum quantization principle to obtain an...
Q10M.9 Consider an HCl molecule. The hydrogen atom irn this molecule has a mass we can look up (see the inside front cover), and the chlorine mass is enough larger that we can (to a first degree of approximation) consider it to be fixed. The bond between these atoms has a local minimum .13 nm, and for "small oscillations" around that minimum, the bond's potential energy can be modeled as a harmonic oscillator potential energy function. Suppose we find that...
2. This problem will help you understand how two atoms can form a molecule through the process of chemical bonding. The physics behind the chemical bonding is very much the same as that discussed in energy splitting process to form energy bands in a macroscopic matter state where we have a lot of atoms involved but all atoms are nicely arranged to form a kind of periodic structure. In this problem, let's make things even simpler: we only consider two...
5. A diatomic molecule (like H2) can be modeled as two atoms of equal mass m, connected by a rigid massless rod of length a. The system is free to rotate in 3-D. I claim the moment of inertia of this molecule around its ceater of mass is a. (Feel free to convince yourself that factor of k is coect!) Big hint if you 're having trouble getting started: this problem is directly related to McIntyre's Ch A) The energy...
A particle with mass m is in a one-dimensional simple harmonic oscillator potential. At time t = 0 it is described by the state where lo and l) are normalised energy eigenfunctions corresponding to energies E and Ey and b and c are real constants. (a) Find b and c so that (x) is as large as possible. b) Write down the wavefunction of this particle at a time t later c)Caleulate (x) for the particle at time t (d)...
Question 8 please
5. We start with Schrodinger's Equation in 2(x,t) = H¥(x,t). We can write the time derivative as 2.4(x, t) = V(x,+) - (xt), where At is a sufficiently small increment of time. Plug the algebraic form of the derivative into Schrodinger's Eq. and solve for '(x,t+At). b. Put your answer in the form (x,t+At) = T '(x,t). c. What physically does the operator T do to the function '(x,t)? d. Deduce an expression for '(x,t+24t), in terms...
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