Problem

Unreasonable Results Red light having a waveleng…

01:15

Problem 17 Medium Difficulty

(a) Calculate the number of photoelectrons per second ejected from a 1.00-mm 2 area of sodium metal by 500-nm EM radiation having an intensity of 1.30 $\mathrm{kW} / \mathrm{m}^{2}$ (the
intensity of sunlight above the Earth’s atmosphere). (b) Given that the binding energy is 2.28 eV, what power is carried away by the electrons? (c) The electrons carry away less power than brought in by the photons. Where does the other power go? How can it be recovered?

Answer

a) $3.27 \times 10^{15}1 / \mathrm{s}$
b)3.204 \times 10^{-20} \mathrm{~J}
c) The other energy goes to the sodium metal to free the electrons that is the binding energy. This power can be recovered by the spontaneous absorption of electrons by sodium metal. Energy of 2.28 eV released for the absorption of an electron.

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Physics 103

College Physics for AP® Courses

Chapter 29

Introduction to Quantum Physics

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Video Transcript

and this problem. We're asked to calculate the number photo electrons per second ejected from a one millimeter squared area of sodium metal by a 500 not a meter. Radiation having an intensity of 1.3 kill ohm kilowatts per meter squared. So for that part, we need to first find the total energy of our wavelength. So we have a TSH, which is planks constant 6.626 times 10 to the negative. 34 Jules time seconds Is the units for the plane constant that we're using? Um V will be the speed of light, which is 2.998 times 10 to the eighth meters per second. Andare wavelength is 500 natto meters, which is 500 times 10 to the negative nine meters. And this gets us a value of 3.973 times 10 to the negative 19. Jules of energy. Now, if we know how much energy are photons have based on the wavelength, then we can use our intensity divided by our energy to figure out how many photons are actually going to be hitting my area. So our intensity is 1.3 kill OEMs Ah, kilowatts. Eso to convert that to just what's its times 10 to the third gets rid of the kilo and this just becomes watts per meter squared, divided by the energy that we just calculated. So that's 3.973 times 10 to the negative 19 again, That's jewels in a what is a Jules per second. So these jewels will counsel and we're left with the number of photons, which is 3.27 to times 10 to the 21 won over seconds meters squared. So again, this is the number of photons per second hitting a square meter area and then the number of ejected electrons per second equals the number of photons per second, hitting the sodium metal. So to find out the number of electrons we can do n times a equals. So this is the number. This is a little and the number of electrons of we want. I'm sorry. The number of photons We want the number of electrons so we can do a three point to seven tomb times 10 to the 21 multiplied by our area. Now our area is one milimeter squared. But we do that need that in meters. So we're going to be converting one 1000 millimetres to a meter and because it is squared, we're going to have to square our conversion as well. And so the most playing all that we get N is equal to 3.27 times 10 to the 15th. And that is our number of ejected electrons per second, which equals the number of photons per second hitting the sodium metal. So again, this isn't a brave electrons for part of it. Four part B and asks us to determined the binding energy, which is 2.28 electron volts using the given binding energy. What power is carried away by the electrons so we can calculate power by first calculating the amount of energy that's carried away by the electrons. So we have kinetic energy equals planks, constant times frequency minus the binding energy will give us our value. So earlier we calculated what basically h times f waas. So this gives us f so h times f was that 3.973 that we calculate earlier and then from that we can subtract Our binding energy now are binding energy is an electron volts. So we need to convert that to Jules so we can get 2.28 electron volts times 1.6 times 10 to the negative. 19 jewels for every one electron volts. Which gets us a kinetic energy off three point 204 times 10 to the negative. 20 Jules again. Now that you have the amount of energy, we actually want to calculate the power. So for power, I'm actually gonna try toe squeezing and up here. So power is equal to n times K. He and this is the value that we calculator earlier. That number of photons So we get 3.272 times tend to the 15. We can multiply it by our energy, which was 3.204 All the times 10 to the negative 20th. Power to get a power of 1.5 times 10 to the negative. Four. What? And for part C, it asks The electrodes carry away less power than brought in by the photons. And it's asking where does the power go and if it can, or how can it be recovered? So for this um the other energy goes to the sodium metal to free the electoral. The binding energy This lost power can be recovered by the spontaneous absorption of electrons by sodium metal. So for each electron absorbed, an energy of 2.28 electron volts will be released.

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