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1) A particle in an infinite well (U = 0, when 0 state (n-1) with an...
5) A particle of mass m is in the ground state of the infinite square well...
5) A particle of mass m is in the ground state of the infinite square well 0 < x < a At t-0 the right hand wall suddenly moves to x = 2a, doubling the size of the well. Assume that this expansion happens on a time scale so fast that the initial wave function (at t0+) is the same as just before the expansion (at t-0-) (This is called the "sudden" approximation.) a) What is the probability that a...
An electron is confined to a one-dimensional infinite well. From experiment, the first excited state is...
An electron is confined to a one-dimensional infinite well. From experiment, the first excited state is measured to have an energy 1.2 eV above the ground state. What must be the width of the well?
4) A particle in an infinite square well 0 for 0
4) A particle in an infinite square well 0 for 0
A particle in an infinite well of width L is in its ground state. a) If...
A particle in an infinite well of width L is in its ground state. a) If L is 30 cm, what is the ground state energy? (3 marks) Where is the particle most likely to be found? Use sketching to further explain. (4 marks)
3. A particle is in a 1D box (infinite potential well) of dimension, a, situated symmetrically ab...
3. A particle is in a 1D box (infinite potential well) of dimension, a, situated symmetrically about the origin of the x-axis. A measurement of energy is made and the particle is found to have the ground state energy: 2ma The walls of the box are expanded instantaneously, doubling the well width symmetrically about the origin, leaving the particle in the same state. a) Sketch the initial potential well making it symmetric about x - 0 (note this is different...
A particle is in the ground state of a symmetric infinite square well with Vx) O...
A particle is in the ground state of a symmetric infinite square well with Vx) O for -a/2<x<+a/2, and infinite elsewhere. (a) The well then undergoes an instantaneous symmetric expansion to -a <<< ta. Calculate the probabilities of the particle being found in each of the three lowest energy states of the larger well. (b) Instead, suppose that the well expansion takes place adiabatically. Again, calculate the probabilities of the particle being found in each of the three lowest energy...
A particle is trapped in an infinite one-dimensional well of width L. If the particle is...
A particle is trapped in an infinite one-dimensional well of width L. If the particle is in it's ground state, evaluate the probability to find the particle: a) between x = 0 and x = L/3 b) between x = L/3 and x = 2L/3 c) between x = 2L/3 and x = L
Suppose that an electron trapped in a one-dimensional infinite well of width 118 pm is excited...
Suppose that an electron trapped in a one-dimensional infinite well of width 118 pm is excited from its first excited state to the state with n = 8. (a) What energy (in eV) must be transferred to the electron for this quantum jump? The electron then de-excites back to its ground state by emitting light, In the various possible ways it can do this, what are the (b) shortest, (c) second shortest, (d) longest, and (e) second longest wavelengths (in...
Consider an electron in an infinite well of width 2.1 nm . What is the wavelength...
Consider an electron in an infinite well of width 2.1 nm . What is the wavelength of a photon emitted when the electron in the infinite well makes a transition from the first excited state to the ground state? The value of h is 1.05457 × 10^−34 J · s, the Bohr radius is 5.29177 × 10^−11 m , the Rydberg constant for hydrogen is 1.09735 × 10^7 m−1 , the ground state energy for hydrogen is 13.6057 eV ,...
An infinitely deep square well has width L 2.5 nm. The potential energy is V =...
An infinitely deep square well has width L 2.5 nm. The potential energy is V = 0 eV inside the well (i.e., for 0 s xs L) Seven electrons are trapped in the well. 1) What is the ground state (lowest) energy of this seven electron system? Eground eV Submit 2) What is the energy of the first excited state of the system? NOTE: The first excited state is the one that has the lowest energy that is larger than...
5) A particle of mass m is in the ground state of the infinite square well 0 < x < a At t-0 the right hand wall suddenly moves to x = 2a, doubling the size of the well. Assume that this expansion happens on a time scale so fast that the initial wave function (at t0+) is the same as just before the expansion (at t-0-) (This is called the "sudden" approximation.) a) What is the probability that a...
An electron is confined to a one-dimensional infinite well. From experiment, the first excited state is measured to have an energy 1.2 eV above the ground state. What must be the width of the well?
4) A particle in an infinite square well 0 for 0
A particle in an infinite well of width L is in its ground state. a) If L is 30 cm, what is the ground state energy? (3 marks) Where is the particle most likely to be found? Use sketching to further explain. (4 marks)
3. A particle is in a 1D box (infinite potential well) of dimension, a, situated symmetrically about the origin of the x-axis. A measurement of energy is made and the particle is found to have the ground state energy: 2ma The walls of the box are expanded instantaneously, doubling the well width symmetrically about the origin, leaving the particle in the same state. a) Sketch the initial potential well making it symmetric about x - 0 (note this is different...
A particle is in the ground state of a symmetric infinite square well with Vx) O for -a/2<x<+a/2, and infinite elsewhere. (a) The well then undergoes an instantaneous symmetric expansion to -a <<< ta. Calculate the probabilities of the particle being found in each of the three lowest energy states of the larger well. (b) Instead, suppose that the well expansion takes place adiabatically. Again, calculate the probabilities of the particle being found in each of the three lowest energy...
Suppose that an electron trapped in a one-dimensional infinite well of width 118 pm is excited from its first excited state to the state with n = 8. (a) What energy (in eV) must be transferred to the electron for this quantum jump? The electron then de-excites back to its ground state by emitting light, In the various possible ways it can do this, what are the (b) shortest, (c) second shortest, (d) longest, and (e) second longest wavelengths (in...
An infinitely deep square well has width L 2.5 nm. The potential energy is V = 0 eV inside the well (i.e., for 0 s xs L) Seven electrons are trapped in the well. 1) What is the ground state (lowest) energy of this seven electron system? Eground eV Submit 2) What is the energy of the first excited state of the system? NOTE: The first excited state is the one that has the lowest energy that is larger than...
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