An electron is confined in a one-dimensional box.Two adjacent allowed energies of the electron are 2.8 × 10^-19 J and 3.5 × 10^-19 J.What is the length of the box? A)1.9 × 10^-9m B)9.3 × 10^-10 m C)1.1 × 10^-9 m D)2.3 × 10^-9 m

Question

Quizplus · Accepted Answer

The energy levels of a particle in a box of length L are given by E_n = (n^2h^2)/(8mL^2), where h is Planck's constant and m is the mass of the particle. 
We are given two adjacent energy levels: 
E_1 = 2.8 × 10^-19 J 
E_2 = 3.5 × 10^-19 J 
We can set these equal to the formula for energy levels and solve for L:

E_1 = (h^2)/(8mL^2) 
L = sqrt((h^2)/(8mE_1)) 
L = sqrt((6.626 x 10^-34 Js)^2 / (8(9.11 x 10^-31 kg)(2.8 x 10^-19 J))) 
L = 1.9 x 10^-9 m

Therefore, the length of the box is 1.9 x 10^-9 m, which corresponds to answer choice A.

An Electron Is Confined in a One-Dimensional Box