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Chapter 34: Problem 23

A red laser at 650 nm and a blue laser at 450 nm emit photons at the same rate. How do their total power outputs compare?

Short Answer

Expert verified
The blue laser has a higher power output compared to the red laser as the energy of photons produced by it is higher despite both of them emitting photons at the same rate.

Step by step solution

01

Calculate the Energy of Photons from the Red Laser

We start by calculating the energy of photons from the red laser using the formula for energy \(E = \frac{hc}{\lambda}\). Here, we use the given value for the wavelength which is 650 nm. Remember to convert the wavelength to meters (since the speed of light is usually given in meters/second) by multiplying by \(1 \times 10^{-9}\).
02

Calculate the Energy of Photons from the Blue Laser

Next, the energy of photons from the blue laser is calculated using the same formula for energy \(E = \frac{hc}{\lambda}\). The given value for the wavelength of the blue laser is 450 nm. As previously, convert this value to meters by multiplying by \(1 \times 10^{-9}\).
03

Compare the Power Outputs

Since the rate of photon emission for both lasers is the same, we do not need to calculate the actual power (which would be \(Power = Energy \times Rate\)). The power outputs of the lasers are directly proportional to their energy outputs, so we just need to compare the two calculated energy values. The higher energy computed would imply a higher power output.

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Most popular questions from this chapter

Find (a) the wavelength and (b) the energy in electronvolts of the photon emitted when a Rydberg hydrogen atom drops from the \(n=180\) level to the \(n=179\) level.

(a) Find the cutoff frequency for the photoelectric effect in copper. (b) Find the maximum energy of the ejected electrons if the copper is illuminated with light of frequency \(1.8 \times 10^{15} \mathrm{Hz}\).

(a) Find the Compton wavelength for a proton. (b) Find the energy in electronvolts of a gamma ray whose wavelength equals the proton's Compton wavelength.

A photocathode ejects electrons with maximum energy \(0.85 \mathrm{eV}\) when illuminated with 430 -nm blue light. Will it eject electrons when illuminated with 633 -nm red light? If so, what will be the maximum electron energy?

The stopping potential in a photoelectric experiment is \(1.8 \mathrm{V}\) when the illuminating radiation has wavelength \(365 \mathrm{nm}\). Determine (a) the work function of the emitting surface and (b) the stopping potential for 280 -nm radiation.
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