Which type of electromagnetic radiation will cause the greatest number of electrons to be ejected from zinc metal with a work function of 350 kJ/mol? (LO 5.4, 5.5) (a) Dim light with a wavelength of 320 nm (b) Dim light with a wavelength of 360 nm (c) Bright light with a wavelength of 360 nm (d) Bright light with a wavelength of 375 nm

Video transcript

Hello everyone today. We are the following problem, which were the following, can eject the most number of electrons from a metal sample. If the work function Of the metal sample is 360 kg per mole. So the first thing we want to recall or do is recall that the work function is the minimum amount of energy needed to eject electrons. So it's the minimum amount of energy used to eject electrons. And so essentially what you wanna do is you want to recall the equation for that. And so that energy That we have about 360 kg joules per mole. We want to convert the killer jewels into regular jewels. And we can note that by doing that. We have 1000 jewels for every one killer jewel. And then we have to use the conversion factor that every one mole contains 6.02 times 10 to the 23rd photons. And so in our units cancel, we're left with 5.98 times 10 to the negative 19th jewels per photon. And we wanna also, before we continue with our calculations, we want to, you know, what would make our answer correct? So the light with a greater energy than our work function will eject the most electrons. So whichever energy is greater than that work function will eject the most electrons. So with anti choice a we have a 385 nanometer wavelength of strong light. So we're gonna go ahead and use the equation, that energy is equal to Planck's constant times the speed of light over the wavelength. And so that's going to look like this. 6.626 times 10 to the negative Times three times 10 to the 8th over our 385 nm. But converted into meters will be one times 10 to the negative 9/1 nanometer. That's going to give us 5.16 times 10 to the negative 19th joules per photon. Is this number greater than or equal to or less than our work function? It's less than so. Answer choice A will not be our answer for B. We are going to go through the same process. Our energy is equal to Planck's constant times the speed of light over our wavelength. We're going to plug in our same variables as before. But this time we're working with 370 nm And that's going to be 10 to the negative 9th meters is equal to one nanometer. One units cancel with 5. times 10 to the negative 19 joules per photon. And is this greater than or equal to our work function? It's going to be less than So answer choice B&C. Will not be our answers because there are both 370 nm of wavelength. And so that leaves answer choice D as our only correct answer. But let's work it out. Energy is equal to Planck's constant times the speed of light over Waverly we plug in our values here, You plug in 330 nm we convert that into meters And we get 6.0196 times 10 to the negative 19th jewels per photon. And we noticed that this is the only number that is greater than our work function. And therefore, since it is greater than our work function, it will eject the most electrons. And with that we have answered our question overall, I hope that this helped and until next time.