an electron in a one dimensional box required a wavelength of 8080 nm to excite an electron from the n=2 to n=3 energy level. calculate the length of the box
To calculate the length of the box, we can use the formula for the wavelength of the photon emitted or absorbed when an electron undergoes a transition between energy levels in a one-dimensional box:
λ = 2L/n
Where:
λ = wavelength of the photon (8080 nm or 8.08 x 10^-6 m)
L = length of the box
n = energy level
Given that the electron transitions from n = 2 to n = 3, we can rearrange the formula to solve for L:
L = λn / 2
L = (8.08 x 10^-6 m) * 3 / 2
L = 1.212 x 10^-5 m
Therefore, the length of the box is 1.212 x 10^-5 meters or 12.12 μm.