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# We want an electron in an infinite well to send out a photon with the energy 3.2 eV when it transits from the third excited state to the?

ground state

(a) What width should the well have?

(b) What color is the transmitted light?

### 1 Answer

- nyphdinmdLv 71 month agoFavorite Answer
For the infinite well the energies of the bound states are given by

E_n = n^2*pi^2*hbar^2/(2mL^2)

Here n = 1, 2, 3, ... and defined w = 2*pi*f = 2*pi*c/wl where f = frequency of photon and wl = awavelength, c = speed of light

Now we want a photon of energy Ep = E_3 - E_1 or

Ep = pi^2*hbar^2/(2mL^2) {(3)^2 - (1)^2} = 8*pi^2*hbar^2^2/(2mL^2)

Re-arrange and solve for L note m = mass of electron = 9.11 x10^-31 kg

L = sqrt(8*pi^2*hbar^2/(2mEp)) = 2*pi*hbar/sqrt(mEp)

Now Ep = 3.2 eV or 5.12x10^-19J, so plugging in we find

L = 6.09 x 10^-9 m = 6.09 nm

THe transmitted light has a wavelength found using Ep = hbar*w = h*f = hc/wl

wl = hc/Ep = 1.3 x 10^-6 m = 1.3 um --> this is in the shortwave infrared

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