Question

For a particle with mass m in a one dimensional box of lenth L, the energy is given by: E n =n 2 h 2 /(8mL 2 ). If the same particle is now placed in another one dimensional box of length L/2, for the same energy level (i.e. the same quantum number n), the energy should be _____ times the energy for the first box.

Answer 1

`E'_n=4* E_n`

Step-by-step explanation:

The energy of a particle in one dimensional box is given by :

`E_n=(n^2h^2)/(8mL^2)`

n is the quantum number

h is the Planck's constant

m is the mass of particle

L is the length of box

If L' = L/2

Energy level is given by :

`E'_n=(n^2h^2)/(8mL'^2)`

`E'_n=(n^2h^2)/(8m(L/2)^2)`

`E'_n=4* (n^2h^2)/(8mL^2)`

`E'_n=4* E_n`

So, if the same particle is placed in another box of length L/2, the energy should be four times the energy for the first box. Hence, this is the required solution.