- #1
mateomy
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An electron is trapped in an infinite one-dimensional well of width 0.251nm. Initially the electron occupies the n=4 state. Suppose the electron jumps to the ground state with the accompanying emission of a photon. What is the energy of the photon?
(Time independent)
What I did was realize that [itex]\psi(x)[/itex] must equal zero at the walls, so I chose [itex]\sin(kL)[/itex] and set it to [itex]n\pi[/itex], then solved for k.
Putting this value of k into the energy for a free particle (Time-ind Schrodinger), I eventually come to the expression:
[tex]
\frac{h^2 n^2}{8mL^2}
[/tex]
To find the corresponding energy of the emitted photon I plugged in the appropriate values of n and solved for the difference.
Does that seem right?
Answer:
[tex]
E=\frac{h^2 15}{8m L^2}
[/tex]
Obviously plugging in appropriate values of m and L afterward.
(Time independent)
What I did was realize that [itex]\psi(x)[/itex] must equal zero at the walls, so I chose [itex]\sin(kL)[/itex] and set it to [itex]n\pi[/itex], then solved for k.
Putting this value of k into the energy for a free particle (Time-ind Schrodinger), I eventually come to the expression:
[tex]
\frac{h^2 n^2}{8mL^2}
[/tex]
To find the corresponding energy of the emitted photon I plugged in the appropriate values of n and solved for the difference.
Does that seem right?
Answer:
[tex]
E=\frac{h^2 15}{8m L^2}
[/tex]
Obviously plugging in appropriate values of m and L afterward.