Chapter 39, Problem 1CQ

To determine

(a)

location where photon is more likely to be detected?

Answer to Problem 1CQ

Solution: Photon is more likely to be found at $x=1\text{m}$.

Explanation of Solution

Given:

Figure of probability density of photons on the x-axis

Figure.1

It is clear from the figure, that the probability of finding a particle at $x=0$ is $0$, and the probability of finding a particle at $x=1$ is 2, since the probability is higher at $x=1$, therefore proton is more likely to be found on $x=1\text{m}$

Conclusion:

Photon is more likely to be found at $x=1\text{m}$.

To determine

(b)

expected number of photons in a 1 mm wide interval at $x=0.50\text{mm}$

Answer to Problem 1CQ

Solution: expected number of photons in a 1 mm wide interval at $x=0.50\text{mm}$ is $1\times {10}^3$

Explanation of Solution

Given:

Figure of probability density of photons on the x-axis

Figure.1

Calculation:

It’s clear from the figure that, probability of finding photon at $x=0.5$ is $1$

The area of curve at x=1 mm is

$\begin{array}{c}A=\frac{1}{2}\times 1\times 2\\ =1\times {10}^{-3}{\text{m}}^{\text{2}}\end{array}$

The expected number of photon that can be detected in the area is

$\begin{array}{c}N=1\times {10}^6\times 1\times {10}^{-3}\\ =1\times {10}^3\end{array}$

Conclusion:

Expected number of photons in a 1 mm wide interval at $x=0.50\text{mm}$ is $1\times {10}^3$