(a) A quantum dot can be modelled as an electron trapped in a cubic three-dimensional infinite square well. Calculate the wavelength of the electromagnetic radiation emitted when an electron makes a transition from the third lowest energy level, E3, to the lowest energy level, E₁, in such a well. Take the sides of the cubic box to be of length L=3.2 x 10-8 m and the electron mass to be me = 9.11 x 10-³1 kg. (b) Specify the degree of degeneracy for each of the E₁ and E3 energy levels, explaining your reasoning.
(a) A quantum dot can be modelled as an electron trapped in a cubic three-dimensional infinite square well. Calculate the wavelength of the electromagnetic radiation emitted when an electron makes a transition from the third lowest energy level, E3, to the lowest energy level, E₁, in such a well. Take the sides of the cubic box to be of length L=3.2 x 10-8 m and the electron mass to be me = 9.11 x 10-³1 kg. (b) Specify the degree of degeneracy for each of the E₁ and E3 energy levels, explaining your reasoning.
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![(a) A quantum dot can be modelled as an electron trapped in a cubic
three-dimensional infinite square well. Calculate the wavelength of the
electromagnetic radiation emitted when an electron makes a transition
from the third lowest energy level, E3, to the lowest energy level, E₁, in
such a well. Take the sides of the cubic box to be of length
L = 3.2 x 10-8 m and the electron mass to be me = 9.11 x 10-³¹ kg.
for each of the E₁ and E3 energy
(b) Specify the degree of degeneracy
levels, explaining your reasoning.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F487d4a57-09e4-477f-9418-372ad0f1abe7%2Fefc855f0-dc10-490b-9062-70ca35770206%2Fnekacuj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(a) A quantum dot can be modelled as an electron trapped in a cubic
three-dimensional infinite square well. Calculate the wavelength of the
electromagnetic radiation emitted when an electron makes a transition
from the third lowest energy level, E3, to the lowest energy level, E₁, in
such a well. Take the sides of the cubic box to be of length
L = 3.2 x 10-8 m and the electron mass to be me = 9.11 x 10-³¹ kg.
for each of the E₁ and E3 energy
(b) Specify the degree of degeneracy
levels, explaining your reasoning.
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Step 1: (a) Know the formula for the energy of a particle in a 3-D infinite potential well.
VIEWStep 2: Write the expression for the energy of the particle in first and third lowest energy level:
VIEWStep 3: Find the expression for the wavelength of the emitted photon.
VIEWStep 4: Calculate the wavelength of the radiation:
VIEWStep 5: (b) Determine the degeneracy of the energy level E1 and E3:
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