Answer :
Question:
A particle is trapped in a 20 nm wide infinite potential well. What is the wavelength of the particle corresponding to n = 7 in nm?
Answer:
[tex]\lambda_n = 5.71\ nm[/tex]
Explanation:
Given
[tex]L = 20nm[/tex] --- the width
[tex]n = 7[/tex]
Required
Determine the wavelength ([tex]\lambda[/tex])
This is calculated as:
[tex]\lambda_n = \frac{2L}{n}[/tex]
Substitute values for L and n
[tex]\lambda_n = \frac{2*20nm}{7}[/tex]
[tex]\lambda_n = \frac{40nm}{7}[/tex]
[tex]\lambda_n = \frac{40}{7}nm[/tex]
[tex]\lambda_n = 5.71428571\ nm[/tex]
[tex]\lambda_n = 5.71\ nm[/tex] --- approximated to 3 significant figures