- #1

Ryaners

- 50

- 2

## Homework Statement

An electron in a one-dimensional box has ground-state energy 2.60 eV. What is the wavelength of the photon absorbed when the electron makes a transition to the second excited state?

## Homework Equations

E

_{n}= n

^{2}h

^{2}/ 8mL

^{2}

hf = hc / λ

⇒ λ = hc / hf

3. The Attempt at a Solution

3. The Attempt at a Solution

The ground-state energy in Joules is (2.60 eV)⋅(1.602⋅10

^{-19}J/eV) = 4.165668⋅10

^{-19}J

First I calculated the length of the box by rearranging the energy level equation above:

L = √(n

^{2}h

^{2}/ 8mE

_{n})

For n=1, this gives:

L = √{(6.626⋅10

^{-34})

^{2}/ 8(9.109⋅10

^{-31})(4.165668⋅10

^{-19})}

= 3.80294⋅10

^{-10}m

Then I used this L to find the energy of the n=2 level:

E

_{n=2}= {(2)

^{2}(6.626⋅10

^{-34})

^{2}} / {8(9.109⋅10

^{-31})(3.80294⋅10

^{-10})

^{2}}

= 1.66627⋅10

^{-18}J

The difference in these energy levels is:

1.66627⋅10

^{-18}J - 4.165668⋅10

^{-19}J = 1.2497⋅10

^{-18}J

I took this to be equal to the energy of the photon absorbed, i.e. equal to hf. Then:

λ

_{photon}= {(6.626⋅10

^{-34})(2.99⋅10

^{8})} / 1.2497⋅10

^{-18}J

= 158.532 nm

I corrected it to 3 significant figures to input the answer; I tried both 159nm and 158nm in case it was a rounding error but Computer Says No. Can anyone spot where I'm going wrong? Thanks in advance!