A particle is in its ground state in a unidimensional potential well with infinitely high walls. Find the force with which the particle acts on the walls. Do the calculations for an electron in a well `10^(-10)` m wide.

Answer

`F=h^(2)//4m_(e)L^(3)=1.2xx10^(-7)N`

Explanation

For a particle in the ground state one de Broglie half-wave fits into the length of the potential well: `L=lamda//2`. The momentum of the particle is `p=h//lamda=h//2L`. The recoil of the particle from the wall of the well is perfectly elastic, so the change in its momentum is `Deltap=2p=h//L`. The average force of pressure is equal to the product of the change in the momentum variation and the number of collisions per unit time:
`F_(av)=Deltap*z=2p(v)/(2L)=p^(2)/(mL)=(h^(2))/(4mL^(3))`