One million photons are detected. what is the expected number of photons in a 1-mm-wide interval at x = 0.50 m ?

Step 1: 
The attached graph represents the probability density of a photon being found (detected) along the horizontal x- axis

Step 2:
We have:
Total number of photons = 1 millions
Now, checking the graph, we will find that:
At x = 0.5, the probability of finding a photon is 1.
To get the probability density at 1 mm wide at the given x value, we will simply multiply the probability with the area under curve as follows:
P(x=0.5) * area under curve = 1 * 1 * 10^-3 = 1 * 10^-3 m^2

Step 3:
Now, we will get the expected number of photons as follows:
N = number of photons * area under curve
N = 1 * 10^6 * 1 * 10^-3
N = 1 * 10³ m²

Hope this helps :)

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