What is the quantum number of an electron confined in a 3.0-nm-long one-dimensional box if the electron's de broglie wavelength is 1.0 nm ? n =?

n = 6

Explanation:

To find the quantum number you use the following formula:

   (1)

n: quantum number

En: energy of the nth state

L: length of the box

hbar = 1,05*10^-34Js

me: mass of the electron = 9.1*10^{-31}kg

Thus, you need to calculate En. To find En you use the wavelength of the electron:

By replacing En and doing n the subject of the formula (1) you obtain:

hence, the quantum number is 6