An electron is in an infinite square well of width a: (U(x)= $\infty$ for x a).If the electron is in the first excited state,Y(x)= Asin(2$\pi$x/a),at what position is the probability function a maximum? A)0 B)a/3 and 2a/3 C)a/4 and 3a/4 D)a/2 E)a

Question

An electron is in an infinite square well of width a: (U(x)= $\infty$ for x < 0 and x > a).If the electron is in the first excited state,Y(x)= Asin(2$\pi$x/a),at what position is the probability function a maximum?
A)0
B)a/3 and 2a/3
C)a/4 and 3a/4
D)a/2
E)a

Quizplus · Accepted Answer

The probability density function for an electron in the nth excited state in an infinite square well of width a is given by:
P(x) = |Y(x)|^2 = A^2sin^2(nπx/a)
The probability density function has the maximum value where the sine function reaches its maximum value, which is 1. The sine function reaches its maximum value at x = nπa/2, where n is an odd integer. Therefore, for the first excited state (n=2), the probability density function has maximum values at x = πa/2 and 3πa/2. The positions of these maxima are a/4 and 3a/4, respectively. Thus, the correct choice is C, a/4 and 3a/4.

An Electron Is in an Infinite Square Well of Width ∞\infty∞

An Electron Is in an Infinite Square Well of Width $\infty$