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Chapter 5: Problem 36

Considering the typical wavelength of light to be \(0.55 \mu \mathrm{m}\), what is a typical photon energy, in Joules, and how many photons per second emerge from a \(1 \mathrm{~W}\) light source? \(^{54}\)

Short Answer

Expert verified
Answer: To find the energy of one photon and the number of photons emitted per second, follow these steps: Step 1: Calculate the energy of one photon using the formula: $$ E = \dfrac{h * c}{\lambda} $$ Plugging in the given values, we get: $$ E = \dfrac{(6.63\times 10^{-34} \text{ Js}) * (3\times 10^8 \text{ m/s})}{0.55\times 10^{-6} \text{ m}} $$ Calculate the energy E. Step 2: Calculate the number of photons emitted per second using the formula: $$ n = \dfrac{P}{E} $$ Plugging in the given values, we get: $$ n = \dfrac{1 \text{ W}}{E} $$ Calculate the number of photons n emitted per second using the energy E found in Step 1.

Step by step solution

01

Find the energy of one photon

To find the energy of one photon, we can use the formula: $$ E = \dfrac{h * c}{\lambda} $$ Plugging in the given values: $$ E = \dfrac{(6.63\times 10^{-34} \text{ Js}) * (3\times 10^8 \text{ m/s})}{0.55\times 10^{-6} \text{ m}} $$ Calculate the energy \(E\).
02

Find the number of photons emitted per second

To find the number of photons emitted per second, we can use the formula: $$ n = \dfrac{P}{E} $$ Plugging in the given values: $$ n = \dfrac{1 \text{ W}}{E} $$ where we already found \(E\), from the previous step. Calculate the number of photons \(n\) emitted per second.

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Most popular questions from this chapter

At what wavelength, in microns \((\mu \mathrm{m})\), is the corresponding photon energy in eV the same number? A deliberately wrong example to illustrate would be if a \(2.6 \mu \mathrm{m}\) wavelength corresponded to \(2.6 \mathrm{eV}\) (it doesn't').

A generic \(\$ 10\) pizza might contain about \(2,500 \mathrm{kcal}\). What is this in \(\mathrm{kWh}\) ? Electricity typically costs \(\$ 0.15\) per \(\mathrm{kWh},{ }^{44}\) so how much would a pizza's amount of energy cost in electrical terms? Which of the two is a cheaper form of energy?

If a microwave operates at a power of \(1,600 \mathrm{~W}(1,600 \mathrm{~J} / \mathrm{s})\), how long will it take to heat \(0.25 \mathrm{~L}\) of water from room temperature to boiling (changing temperature by \(80^{\circ} \mathrm{C}\) ) if \(50 \%\) of the microwave energy is absorbed by the water?

A couch might take \(100 \mathrm{~N}\) to slide across a floor. If someone slides the couch 4 meters and does it in 8 seconds, how much power did they expend?

A typical textbook may have a mass of \(1 \mathrm{~kg}\), and thus a weight of about \(10 \mathrm{~N}\). How high could the textbook be lifted (against the force of gravity) by supplying one Joule of energy?
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