91影视

The lowest transition of the electron produces a photon of wavelength.

Formula used:

The expression for the difference in energy levels is given by

$\mathbf{螖贰}\mathbf{=}{\mathbf{E}}_{\mathbf{2}}\mathbf{-}{\mathbf{E}}_{\mathbf{1}\mathbf{}}$

Here,$E_2$and$E_1$are the energy of the highest and lowest energy levels, respectively.

The expression for the energy of thenthlevel is given by

$E_n=\frac{n^2{h}^2{蟺}^2}{2m{L}^2}$

Here,nis the number of energy levels.,Is reduced Planck鈥檚 constant,$\mathrm{鈩�}=h^2蟺$.

h is Planck鈥檚 constant,$h=6.64脳{10}^{-34}\text{J}路\text{s}$,m is the mass of an electron$9.1脳{10}^{-31}\text{kg}$, andLis the width of the quantum well.

Determine the equation in terms of the width of the quantam well as:

$\begin{array}{rcl}\frac{hc}{位}& =& \frac{2^2{蟺}^2{h}^2}{2m{L}^2}-\frac{1^2{蟺}^2}{2m{L}^2}\\ \frac{hc}{位}& =& \frac{3{蟺}^2{h}^2}{2m{L}^2}\\ L& =& \sqrt{\frac{3{蟺}^{2}h位}{8{蟺}^{2}mc}}\\ & & \end{array}$

Substitute the values and solve as:

$\begin{array}{rcl}L& =& \sqrt{\frac{3{蟺}^{2}h位}{8{蟺}^{2}mc}}\\ & =& \sqrt{\frac{3{蟺}^2\left(6.625脳{10}^{-34}\right)\left(450脳\frac{1}{{10}^9}\right)}{8{蟺}^2\left(9.1脳{10}^{-31}\right)\left(3.0脳{10}^8\right)}}\\ & =& 0.64\text{nm}\\ & & \end{array}$

The width of the quantum well in which an electron is trapped, which produces a photon of wavelength for its lowest transition is$6.4脳{10}^{-10}\text{m}$