- #1
Ryaners
- 50
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I don't know where I'm going wrong with this problem - I was so sure I had it right but the online grader tells me otherwise 
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?
En = n2h2 / 8mL2
hf = hc / λ
⇒ λ = hc / hf
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 = √(n2h2 / 8mEn)
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:
En=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:
λphoton = {(6.626⋅10-34)(2.99⋅108)} / 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!
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
En = n2h2 / 8mL2
hf = hc / λ
⇒ λ = hc / hf
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 = √(n2h2 / 8mEn)
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:
En=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:
λphoton = {(6.626⋅10-34)(2.99⋅108)} / 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!