An electron is trapped in a one dimensional
infinite potential well of width 18. How much
energy must be supplied to excite it from
ground state to first excited state.
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1
Answer:
The probability that the electron is found in any interval is given by P=∫∣ψ∣
2
dx. where the integral is over the interval. If the interval width Δx is small, the probability can be approximated by P=∣ψ∣
2
Δx, where the wave functions is evaluated for the center of the interval say. For an electron trapped in an infinite well of width
L, the ground state probability density is
∣ψ∣
2
=
L
2
sin
2
(
L
πx
)
P=(
L
2Δx
)sin
2
(
L
πx
)
We take L=100 pm,x=90 pm, and Δx=5.0 pm. Then,
P=[
100 pm
2(5.0 pm)
]sin
2
[
100 pm
π(90 pm)
]=0.0095.
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