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 wavelength of the box
The formula for the wavelength of light required to excite an electron from one energy level to another in a one dimensional box is:
λ = 2L/n,
where λ is the wavelength, L is the length of the box, and n is the energy level.
In this case, the electron moved from the n=2 to the n=3 energy level, and the wavelength required was 8080 nm. So we can set up the equation:
8080 = 2L/2.
Solving for L:
8080 = 2L/2,
16160 = L.
Therefore, the length of the box is 16160 nm.
To find the wavelength of the box when an electron moves from the n=1 to n=2 energy level, we use the formula with n=1:
λ = 2(16160)/1,
λ = 32320 nm.
So, the wavelength of the box when an electron moves from the n=1 to n=2 energy level is 32320 nm.