FIGURE Q39.1 shows the probability density for photons to be detected on the $x$-axis.

1. Is a photon more likely to be detected at $x=0\text{m}$ or at $x=1\text{ m}?$ Explain.

2. One million photons are detected. What is the expected number of photons in a 1-mm-wide interval at $x=0.50\text{m}?$

FIGURE Q39.1

What is the difference between the probability and the probability density?

For the electron wave function shown in FIGURE Q39.3, at what position or positions is the electron most likely to be found? Least likely to be found? Explain.

FIGURE Q39.3

FIGURE Q39.4 shows the dot pattern of electrons landing on a screen.

1. At what value or values of $x$ is the electron probability density at maximum? Explain.

2. Can you tell at what value or values of $x$ the electron wave function $\psi \left(x\right)$ is most positive? If so, where? If not, why not?

FIGURE Q39.4

What is the value of the constant $a$ in FIGURE Q39.5?

FIGURE Q39.5

FIGURE Q39.6 shows wave packets for particles 1, 2, and 3. Which particle can have its velocity known most precisely? Explain.

FIGURE Q39.6