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

Length will be 0.491 nm

Step-by-step explanation:

We have given wavelength of the photon
`\lambda =800nm=800* 10^(-9)m`

Plank's constant
`h=6.6* 10^(-34)J-s`

We know that energy of the photon is given by

`E=(hc)/(\lambda )=(6.6* 10^(-34)* 3* 10^8)/(800* * 10^(-9))=2.475* 10^(-19)J`

We know that energy of photon is also given by

`E=(n^2h^2)/(8mL^2)=(h^2)/(8mL^2)`

`2.475* 10^(-19)=((6.6* 10^(-34))^2)/(8* 9.1* 10^(-31)* L^2)`

`L=0.491* 10^(-9)m`