Question

g A particle is trapped in a 20 nm wide infinite potential well. What is the wavelength of the particle corresponding to n

Answer 1

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:

$\lambda_n = 5.71\ nm$

Explanation:

Given

$L = 20nm$ --- the width

$n = 7$

Required

Determine the wavelength ($\lambda$)

This is calculated as:

$\lambda_n = \frac{2L}{n}$

Substitute values for L and n

$\lambda_n = \frac{2*20nm}{7}$

$\lambda_n = \frac{40nm}{7}$

$\lambda_n = \frac{40}{7}nm$

$\lambda_n = 5.71428571\ nm$

$\lambda_n = 5.71\ nm$ --- approximated to 3 significant figures