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1. Infinite potential quantum well. (1) Starting from the Schrödinger equation, please derive the...
Consider the electron states in an infinite square well potential. a) If the difference in energy...
Consider the electron states in an infinite square well potential. a) If the difference in energy between the n=2 and the n=3 states is 2 eV, calculate the width of this square well. b) If energy making a transition from the n=3 state to the n=2 state gives up the energy difference as an emitted photon, what is the wavelength of the photon?
5. Electron in an Infinite Potential Well a) Calculate the ground state and two next highest...
5. Electron in an Infinite Potential Well a) Calculate the ground state and two next highest energy levels for an electron confined to an infinitely high potential well of width l = 1.00E-10 m (roughly the diameter of a hydrogen atom in its ground state). b) If a photon were emitted when an electron jumps from n = 2 to n = 1, what would it's wavelength be? In which part of the spectrum does this lie?
1. Consider a particle of mass m in an infinite square well with potential energy 0...
1. Consider a particle of mass m in an infinite square well with potential energy 0 for 0 Sz S a oo otherwise V (x) For simplicity, we may take the 'universe' here to be the region of 0 S z S a, which is where the wave function is nontrivial. Consequently, we may express stationary state n as where En is the associated mechanical energy. It can be shown that () a/2 and (p:)0 for stationary state n. (a)...
clear hand written please 2. The nuclear potential that binds protons and neutrons in the nucleus of an atom is often approximated by a square well. Imagine a proton confined in an infinite square...
clear hand written please
2. The nuclear potential that binds protons and neutrons in the nucleus of an atom is often approximated by a square well. Imagine a proton confined in an infinite square well of a length10nm. What is the wavelength of a photon emitted when this proton moves from the n-2 energy state to the n-1 energy state. In what region of the electromagnetic spectrum is this photon and does this make sense in terms of nuclear spectroscopy?...
6. Consider an electron in an infinite potential well of size 1 nm (a) What is...
6. Consider an electron in an infinite potential well of size 1 nm (a) What is the ground state (lowest energy level) energy of the electron? (b) What is the energy required to move an electron from ground state to the third energy level (n-3)? (c) What wavelength of photon would be emitted if the electron move from n-3 to its ground level? (Electron mass - 9.11 x 103 kg, h-1.055 x 1034 J.s, h 6.626 x 1034 J.s)
Q4. Consider the 1D infinite square-well potential shown in the figure below. V(x) O0 Position (a)...
Q4. Consider the 1D infinite square-well potential shown in the figure below. V(x) O0 Position (a) State the time-independent Schrödinger equation within the region 0<x<L for a particle with positive energy E 2 marks] (b) The wavefunction for 0<x< L can be written in the general form y(x) = Asin kx + B cos kx. Show that the normalised wavefunction for the 1D infinite potential well becomes 2sn'n? ?snT/where ( "1,2,3 ! where ( n = 1,2,5, ). [4 marks]...
Suppose that an electron is trapped in a one- dimensional, infinite potential well of width 250...
Suppose that an electron is trapped in a one- dimensional, infinite potential well of width 250 nm is excited from the 2nd excited state to the fifth excited state. What energy must be transferred to the electron in order to make this transition? Answer: 1.62 x 10^-4 eV Check Correct Marks for this submission: 2.00/2.00. What wavelength photon does this correspond to? Answer: 75.15*10^-4m Check Considering all of the possible ways that the excited electron can de-excite back down to...
An electron is trapped in an infinite square-well potential of width 0.3 nm. If the electron...
An electron is trapped in an infinite square-well potential of width 0.3 nm. If the electron is initially in the n = 4 state, what are the various photon energies that can be emitted as the electron jumps to the ground state? (List in descending order of energy. Enter 0 in any remaining unused boxes.) highest eV eV eV eV eV lowest eV
please show work on paper 1.1 (opts). When the electron in a hydrogen atom falls from...
please show work on paper
1.1 (opts). When the electron in a hydrogen atom falls from an excited energy level to the third energy level, a photon with a wavelength of 1005 3 nm is emitted. What is the principle quantum number of the original state?
A particle with a mass of 12 mg is bound in an infinite potential well of...
A particle with a mass of 12 mg is bound in an infinite potential well of width a 1 cm. The energy of the particle is 10 m3. (a) Determine the value of n for that state. what is the energy of the (n + 1) state? (c) Would quantum effects be observable for this particle?
1. Consider a particle of mass m in an infinite square well with potential energy 0 for 0 Sz S a oo otherwise V (x) For simplicity, we may take the 'universe' here to be the region of 0 S z S a, which is where the wave function is nontrivial. Consequently, we may express stationary state n as where En is the associated mechanical energy. It can be shown that () a/2 and (p:)0 for stationary state n. (a)...
clear hand written please
2. The nuclear potential that binds protons and neutrons in the nucleus of an atom is often approximated by a square well. Imagine a proton confined in an infinite square well of a length10nm. What is the wavelength of a photon emitted when this proton moves from the n-2 energy state to the n-1 energy state. In what region of the electromagnetic spectrum is this photon and does this make sense in terms of nuclear spectroscopy?...
6. Consider an electron in an infinite potential well of size 1 nm (a) What is the ground state (lowest energy level) energy of the electron? (b) What is the energy required to move an electron from ground state to the third energy level (n-3)? (c) What wavelength of photon would be emitted if the electron move from n-3 to its ground level? (Electron mass - 9.11 x 103 kg, h-1.055 x 1034 J.s, h 6.626 x 1034 J.s)
Q4. Consider the 1D infinite square-well potential shown in the figure below. V(x) O0 Position (a) State the time-independent Schrödinger equation within the region 0<x<L for a particle with positive energy E 2 marks] (b) The wavefunction for 0<x< L can be written in the general form y(x) = Asin kx + B cos kx. Show that the normalised wavefunction for the 1D infinite potential well becomes 2sn'n? ?snT/where ( "1,2,3 ! where ( n = 1,2,5, ). [4 marks]...
Suppose that an electron is trapped in a one- dimensional, infinite potential well of width 250 nm is excited from the 2nd excited state to the fifth excited state. What energy must be transferred to the electron in order to make this transition? Answer: 1.62 x 10^-4 eV Check Correct Marks for this submission: 2.00/2.00. What wavelength photon does this correspond to? Answer: 75.15*10^-4m Check Considering all of the possible ways that the excited electron can de-excite back down to...
An electron is trapped in an infinite square-well potential of width 0.3 nm. If the electron is initially in the n = 4 state, what are the various photon energies that can be emitted as the electron jumps to the ground state? (List in descending order of energy. Enter 0 in any remaining unused boxes.) highest eV eV eV eV eV lowest eV
please show work on paper
1.1 (opts). When the electron in a hydrogen atom falls from an excited energy level to the third energy level, a photon with a wavelength of 1005 3 nm is emitted. What is the principle quantum number of the original state?
A particle with a mass of 12 mg is bound in an infinite potential well of width a 1 cm. The energy of the particle is 10 m3. (a) Determine the value of n for that state. what is the energy of the (n + 1) state? (c) Would quantum effects be observable for this particle?
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