If a particle is confined to a one-dimensional box of length 300 pm, for $\Psi$₃ the particle has zero probability of being found at A) 100 and 200 pm, respectively. B) 150 pm only. C) 50, 150, and 250 pm, respectively. D) 50 and 250 pm, respectively. E) 75, 125, 175, and 225 pm, respectively.

Question

Quizplus · Accepted Answer

In a one-dimensional box, a particle has zero probability of being found at the nodes of its wave function. The locations of these nodes depend on the quantum state of the particle. For the ground state (n=1), there are no nodes inside the box, meaning the particle has a non-zero probability of being found anywhere inside the box except at the walls. For excited states (n>1), nodes appear at specific positions. However, none of the options provided directly correspond to the nodes for a specific quantum state without additional context. The question seems to be incorrectly formatted or missing crucial information regarding the quantum state of the particle. However, assuming a typical interpretation of quantum mechanics, no option correctly describes the node positions for a given state without specifying the state's quantum number. Thus, the response is based on the assumption that the question intended to ask about a scenario not accurately represented by the options given.

If a Particle Is Confined to a One-Dimensional Box of Length