Question

What is the length of a one-dimensional box in which an electron in the n=1 state has the same energy as a photon with a wavelength of 800 nm ?

Answer 1

Answer:

Length will be 0.491 nm

Explanation:

We have given wavelength of the photon $\lambda =800nm=800\times 10^{-9}m$

Plank's constant $h=6.6\times 10^{-34}J-s$

We know that energy of the photon is given by

$E=\frac{hc}{\lambda }=\frac{6.6\times 10^{-34}\times 3\times 10^8}{800\times \times 10^{-9}}=2.475\times 10^{-19}J$

We know that energy of photon is also given by

$E=\frac{n^2h^2}{8mL^2}=\frac{h^2}{8mL^2}$

$2.475\times 10^{-19}=\frac{(6.6\times 10^{-34})^2}{8\times 9.1\times 10^{-31}\times L^2}$

$L=0.491\times 10^{-9}m$