In this precedent, we calculate the threshold frequency and bind power from the kinetic energy of an spewed electron and the wavelength of electromagnetic radiation striking a metal. Our problem speaks, “When a photon with a wavelength of 242 nm strikes the surface of a metal, the spewed electrons have a kinetic energy of 3.31 electron volts. Note: 1 electron volt is 1.602 x 10^ -1 9 joules. Place A: calculate the binding intensity of the metal in joules. Place B: calculate the binding force in kilojoules per mole. Side C: calculate the threshold frequency of the metal. First let’s look at the photoelectric effect and the equations and govern it. In the photoelectric effect, an electron in a metal is assimilate a photon and is subsequently ejected from the metal if the photon has sufficient energy.We can calculate the force of a photon striking the metal with either the frequency or wavelength of the photon. The vitality of the photon equals H C over lambda, which is Planck’s constant goes the speed of light divided by wavelength. Or if we have frequency, the power of the photon is equal to H nu, which is Planck’s constant ages frequency. The electron has some vitality retaining it in the metal, which is called the binding energy or phi. This is the energy that must be overcome to eject the electron from the metal. If we start with a small energy for the photon striking the metal and slowly increase it, at some detail the photon will have just enough energy to expel the electron.At this level we’re at the threshold frequency: when we just start to eject electrons from the metal. The intensity of the photon striking the metal is Planck’s constant hours the threshold frequency which is our equation for binding power. If we continue to increase the energy of the photon beyond the threshold frequency, we’re adding extra vitality to the electron. Since vigor cannot be created or destroyed, any extra vigor beyond the binding vigor goes into the kinetic energy of the spewed electron. So to calculate the kinetic energy, we subtract the fastening vigour from the vigour of the photon.In part A of our question, we’re asked to find the binding energy of the metal and we’re given the kinetic energy of the spewed electron. We’ll need to use the kinetic energy equation. We’re also given the wavelength of the photon, so we’ll use H C over lambda to calculate the energy of the photon in that equation. In part B, we’re asked to change the units of the binding power from joules to kilojoules per mole of electrons. We can do this using dimensional analysis. In part C, we’re asked to find the threshold frequency of the metal.We can be utilized our binding intensity equation to solve for doorstep frequency. Now that we have a plan let’s get started with the math. For fraction A, we start with the kinetic energy equation and we answer for fixing energy. Binding energy equals the vitality of the photon that strikes the metal subtract the kinetic energy of the electron. To answer for the force of photon, we use H C over lamdba because we’re held wavelength of the photon. We can plug in Planck’s constant and the speed of light. When we compute the wavelength to this the equation, it needs to be in meters instead of nanometers. “Nano” implies 10 to the negative ninth so 242 nm is 242 epoch 10 to the negative ninth rhythms. Answering this equation, we get 8.209 ages 10 to the -1 9th joules. We can replace this into our equation at the top; the next step is to find kinetic energy. We’re contributed kinetic energy in their own problems, but we can’t alternative it into the equation in electron volts: we need joules.To convert from electron volts to joules we use dimensional analysis. We’re considering the fact that 1 electron volts equals 1.602 meters 10 to the -1 9th joules in their own problems. Completing the estimation, we get 5.303 meters 10 to the -1 9th joules for the kinetic energy of the electron. We can replace this numeral into our equation at the top. Solving for obliging energy, we get 2.906 epoches 10 to the -1 9th joules; this evaluate is the binding energy for a single electron. In part B, we want to convert the human rights unit for the bind exertion to kilojoules per mole of electrons. We can do this using dimensional analysis. We’ll start our dimensional analysis with 2.906 durations 10 to the -1 9th joules per one electron.We can alter from joules to kilojoules exercising metric prefixes and from electrons to moles of electrons employing Avogadro’s count. Completing the computation, the binding intensity is 175 kilojoules per mole. Binding vitalities of metals are often given in cells of kilojoules per mole because they’re easier to work with. In part C, we’re forecast the threshold frequency from the binding intensity. Rearranging our equation to solve for threshold frequency, we get fixing force divided by Planck’s constant. For this equation we need to use the binding energy in joules for one electron , not kilojoules per mole. Substituting in the binding exertion and Planck’s constant, we get 4.39 seasons 10 to the 14 th. The units are 1 divided among seconds, which are also hertz ..
