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Chapter 36: Problem 67

A nocturnal bird's eye can detect monochromatic light of frequency \(5.8 \cdot 10^{14} \mathrm{~Hz}\) with a power as small as \(2.333 \cdot 10^{-17} \mathrm{~W}\). What is the corresponding number of photons per second a nocturnal bird's eye can detect?

Short Answer

Expert verified
Answer: A nocturnal bird's eye can detect about 61 photons per second.

Step by step solution

01

Write down the given values

We have the following given values: Frequency of light (f) = \(5.8 \cdot 10^{14} Hz\) Minimum power detected (P) = \(2.333 \cdot 10^{-17} W\)
02

Calculate the energy per photon

We can calculate the energy per photon (E) using Planck's equation: E = hf Where E is the energy per photon, h is Planck's constant (\(6.626 \cdot 10^{-34} Js\)), and f is the frequency of the light. Substituting the given values, we get: E = \((6.626 \cdot 10^{-34} Js)(5.8 \cdot 10^{14} Hz)\) E = \(3.84308 \cdot 10^{-19} J\)
03

Calculate the number of photons per second

Now, we can use the equation: Number of photons per second = (Power detected) / (Energy per photon) Substituting the given values and the calculated energy per photon, we get: Number of photons per second = \(\frac{2.333 \cdot 10^{-17} W}{3.84308 \cdot 10^{-19} J}\) Number of photons per second = \(6.072 \cdot 10^1\) So, a nocturnal bird's eye can detect about 61 photons per second.

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