Question

particle of mass m is confined in a field free region between impenetrable walls at x=0 and x=r. Show that the stationary energy levels of the particle is given by Eu=u²π²h²/2mr² where u =1,2,3

Answer 1

For u = 1, 2, 3, the energy levels would be E1 = π²h²/2mr², E2 = 4π²h²/2mr², and E3 = 9π²h²/2mr².

Step-by-step explanation:

In the case of a particle confined between impenetrable walls at x=0 and x=r, the potential energy is zero between the walls and infinite outside the walls. This setup is known as the infinite square well. The stationary energy levels of the particle in the well can be calculated using the Schrodinger equation.

The energy levels are given by the formula Eu = u²π²h²/2mr², where u represents the quantum number of the energy level. For u = 1, 2, 3, the respective energy levels would be E1 = π²h²/2mr², E2 = 4π²h²/2mr², and E3 = 9π²h²/2mr².