#
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.

## Answers

Answered by

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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