The amount of energy necessary to remove an electron from an atom is a quantity called the ionization energy, Ei. This energy can be measured by a technique called photoelectron spectroscopy, in which light of wavelength l is directed at an atom, causing an electron to be ejected. The kinetic energy of the ejected electron (Ek) is measured by determining its veloc-ity, v (Ek = mv2/2), and Ei is then calculated using the conservation of energy principle. That is, the energy of the incident light equals Ei plus Ek. What is the ionization energy of selenium atoms in kilojoules per mole if light with l = 48.2 nm produces electrons with a velocity of 2.371 * 106 m/s? The mass, m, of an electron is 9.109 * 10-31 kg.

Video transcript

Hello everyone today. We have the following problem. The ionization energy abbreviated I, is the amount of energy required to expel an electron from an atom in this process known as photoelectron spectroscopy and electron is ejected from an atom. When lightwave light of wavelength L. Is directed at it along for the measurement of this energy. After calculating the velocity of the ejected electron given by this following formula and its kinetic energy K. The conservation of energy principle is used to calculate i in other words are ionization energy plus our kinetic energy equals the energy of the incident light. Considering that light has a wavelength of 53.7 nanometers causes electrons to move at a speed of 1.238 times 10 to the sixth meters per second. What is the ionization energy of germanium atoms in kilograms per mole. The mass of an electron is nine point oh 9.1 oh nine times 10 to the negative 31 kg. So the very first thing that we have to do when approaching this problem is convert Our Nanometers two m. And so according to the question, we have 53.70 nm And we can convert this to regular meters by using the conversion factor, that one nanometer is equal to one times 10 to the negative nine m. When our units cancel, we're left with 5.37 times 10 to the negative eight meters. And we'll hang on to this number here. Our 2nd step is to calculate our energy or e the energy of a photon and the energy of a photon is equal to Planck's constant times the speed of light over the wavelength. And so when we plug those values in planks constant is 6.626 times 10 to the negative 30 for jules. Time second Times the speed of light which is three times 10 to the 8th m/s over Our wavelength, which was 5.37 times 10 to the negative eight m that we just calculated. And then we have to do some conversions here Because we need this in units of killer jewels and we have jewels in the numerator. So we use a conversion factor, that one kg jule is equal to 1000 jewels. And then of course we use avocados number right here, six point oh 22 times 10 to the 23rd everyone. And when we do this, we end up with 2229.15 kg joules per mole. And so we'll hang on to that number for later we then have to calculate our kinetic energy which is equal to one half times the mass times our velocity squared. And so when we plug those numbers, in we have one half times our mass that we have of an electron which is 9.109 times 10 to the negative kilograms. We then multiply that by our velocity. So we see that we have a speed right here of 1.238 times 10 to the six m per second squared. Once again, we want this in units of kilograms per mole. So we are going to have to do some math here First. We're going to use the conversion factor that one killer jewel is equal to 1000 jewels. And then we're going to use the conversion factor that everyone mole has six point oh 22 times 10 to the 23rd atoms or ions. And when our units cancel, we get 420 0.36 kg joules per mole. And so we'll save that number for our last and final step here, which it was stated that the ionization energy plus our kinetic energy is going to be equal to the energy of the incident light. And so this is essentially going to be equal to the following. Our ionization energy will be equal to the energy of a photon minus our kinetic energy. And so we plug those values in. We get our 2229.15 kg joules per mole. And we subtract that by our 420. kil joules per mole. And we get a final answer of 1,808.79 kg joules per mole. Ultimately, we have solved the problem, I hope this helped. And until next time