Question

In an interference experiment with electrons, you find the most intense fringe is at x = 7.0 cm. There are slightly weaker fringes at x= 6.0 and 8.0 cm, still weaker fringes at x = 4.0 and 10.0 cm, and two very weak fringes at x= 1.0 and 13.0 cm. No electrons are detected at x <0 cm or x> 14 cm.

a. Sketch a graph of $\left|\psi \right(x){|}^2$is for these electrons.

b. Sketch a possible graph of $\psi \left(x\right)$.

c. Are there other possible graph for$\psi \left(x\right)$? If so draw one

Short answer

Therefore, the graphs of the functions are drawn.

Step-by-step solution

Given information

In an interference experiment with electrons, you find the most intense fringe is at x = 7.0 cm. There are slightly weaker fringes at x= 6.0 and 8.0 cm, still weaker fringes at x = 4.0 and 10.0 cm, and two very weak fringes at x= 1.0 and 13.0 cm. No electrons are detected at x <0 cm or x> 14 cm.

Explanation

a) Because the graph will be used to represent the likelihood of finding an electron at position (c), all points on the graph must be either zero or positive. According to the given data, the graph's greatest peak will be at x = 7, the probability then decays and rises again at x = 8 but with a smaller peak, and decays and rises again at x = 10 with a peak smaller than those at x = 8 and 7, one more decay of the probability before it rises at x = 13 with the smallest peak of all the peaks, and finally decays to zero without any peaks at x > 13, and finally decays to zero. The other side of the graph, especially for x<7, is an image of the graph for x> 7, as shown below, due to the symmetry of the information presented in the problem.

Explanation

b and c) When creating the wave function graph, remember that the values of $\psi \left(x\right)$are the square roots of the values on the localid="1648592523486">|ψ(x)|2, so the peaks of the graph of $\psi \left(x\right)$will be smaller than those of $\left|\psi \right(x){|}^2$. Another key consideration is to draw $\psi \left(x\right)$so that it oscillates between positive and negative values each time it crosses the x-axis, resulting in two alternative graphs of $\left|\psi \right(x){|}^2$, as shown below.