Question

20.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$1.0\mathrm{nm}$ ?

Short answer

The Quantum number of the electron is$n=6$

Step-by-step solution

Step: 1 Given information

3.0-nm-long one-dimensional box if the electron's de Broglie wavelength is $1.0\mathrm{nm}$

Step: 2 Calculation 

We can start the solution with expression for de Broglie wavelength of a particle in a box:

$$\begin{gathered} \lambda =\frac{2L}{n} \\ n=\frac{2L}{{\lambda }_n} \\ n=\frac{2·3·{10}^{-9}}{1·{10}^{-9}} \\ n=6 \end{gathered}$$