2. Confined Particles (1) Energy is required to compress the box when a particle is inside: this suggests that the particle exerts a force on the walls. (a) On the basis that when the length of the box changes by dL the energy changes by dE=FdL, find an expression for the force. (b) At what length does F=1N when an electron is in the state n=1 ? (2) A particle is in a linear box that is 1nm in length. What is the probability that a particle is between 0.45nm and 0.55nm in the ground state? The normalized wavefunction for the particle is given below. n=(2/a)1/2sin(nx/a), where a is the length of the box. (3) A particle is faced with the potential barrier whose potential energy shown in the figure below. What is the solution to the Schrodinger equation in each region when 0