A particle of mass 2.00×10^−10 kg is confined in a hollow cubical three-dimensional box, each edge of which has a length, 2.00×10^−10 m, and for which the potential energy function is zero inside, and infinite outside, the box. The total energy of the particle is 2.47×10^−37 J. What are the quantum numbers that correspond to each of the three possible quantum states?

(b) (i) If the same particle is instead confined in one dimension between infinitely high potential barriers, with the same energy and in the same size region as above, what is the single quantum number that characterises the wavefunction of the particle when it occupies this energy level?
(ii) Explain why the particle is more likely to be detected in a small region centred on a position 0.50×10^−10 m from either wall than in a small region centred on a position 1.00×10^−10 m from either wall.