Kinetic Energy and Work
This freed electron is usually referred to now as a photoelectron. So one photon creates one photoelectron. So one particle hits another particle. And, if you think about this in terms of classical physics, you could think about energy being conserved.
So the energy of the photon, the energy that went in, so let me go ahead and write this here, so the energy of the photon, the energy that went in, what happened to that energy?
Some of that energy was needed to free the electron. So the electron was bound, and some of the energy freed the electron. I'm gonna call that E naught, the energy that freed the electron, and then the rest of that energy must have gone into the kinetic energy of the electron, and so we can write here kinetic energy of the photoelectron that was produced.
So, kinetic energy of the photoelectron. So let's say you wanted to solve for the kinetic energy of that photoelectron. So that would be very simple, it would just be kinetic energy would be equal to the energy of the photon, energy of the photon, minus the energy that was necessary to free the electron from the metallic surface.
And this E naught, here I'm calling it E naught, you might see it written differently, a different symbol, but this is the work function. Let me go ahead and write work function here, and the work function is different for every kind of metal.
So, it's the minimum amount of energy that's necessary to free the electron, and so obviously that's going to be different depending on what metal you're talking about. All right, let's do a problem. Now that we understand the general idea of the Photoelectric effect, let's look at what this problem asks us.
So the problem says, "If a photon of wavelength " nm hits metallic cesium So we know what E naught is here.
Kinetics • Relation between work and energy
What we don't know is the energy of the photon so that's what we need to calculate first. And so the energy of the photon, energy of the photon, is equal to h, which is Planck's constant, times the frequency, which is usually symbolized by nu.
So, we got the frequency, but they gave us the wavelength in the problem here. They gave us wavelength, so we need to relate frequency to wavelength, and that's related by c, which is the speed of light, is equal to lambda times nu. So, c is the speed of light, and that's equal to the frequency times the wavelength. So we can substitute n for the frequency, all right, 'cause we just use this equation and say that the frequency is equal to the speed of light divided by the wavelength.
The frequency is equal to speed of light over lambda, so we can plug that into here, and so now we have the energy of the photon is equal to hc over lambda, and we can plug in those numbers.
So, times 10 to the negative 34 here. Lambda is the wavelength. So times 10 to the negative 9th meters. All right, so let's get out our calculator and calculate the energy of the photon here. So, let's go ahead and do that math, so we have 6. We're gonna divide it by the wavelength, times 10 to the negative 9, and we get 3.
So, let me go ahead and write that down here.
What are energy and work?
And that energy of the photon is greater than the work function, which means that that's a high-energy photon. It's able to knock the electron free, 'cause remember, this number right here, is the minimum amount of energy needed to free the electron and so we've exceeded that minimum amount of energy, and so we will produce a photoelectron. So, this photon is high-energy enough to produce a photoelectron.
So let's go ahead and find the kinetic energy of the photoelectron that's produced. So we're gonna use this equation right up here.
Photoelectric effect (video) | Photons | Khan Academy
So let me just go and get some more room, and I will rewrite that equation. In order to maximize kinetic energy of human body or sport equipment we must exert the greatest possible force along the longest possible distance.
This way we can make us of the knowledge of the relation between energy and work to improve our technique in certain sports, especially in athletics. According to the relation between work and energy the velocity is maximized by the greatest possible force acting along the longest possible distance. Shot-putters therefore often start their throw by standing on one foot, bent forward over the edge of the shot-put circle, with their back towards the direction of the throw, to maximize the distance along which their force will act on the shot and thus to also maximize the initial velocity of the shot at the moment of the throw Fig.
The longer distance along which the force acts on the shot and the ability to use larger muscle groups thus leads to longer throws and better results.
Figure 13 Initial phases of shot put allowing to maximize the work performed during the throw. This happens mostly in catching projectiles, landing, etc. Human muscles also perform negative work when our body lands on the ground.
During landing it is important to maximize the distance along which the projectile is decelerating. By making stopping distance longer we make impact forces smaller.
We must realize, however, that prolonging the stopping distance by bending our knees deeply, for example, does not necessary lead to smaller reaction forces in specific joints. To decrease impact forces and increase stopping distance we also use various materials: This law can be used in studying the motion of projectiles.
- Photoelectric effect
This kinetic energy is transformed into deformation energy of the pole and subsequently into the increase in potential energy of the athlete. In other words, the faster the pole vaulter runs and the better his pole is able to transform kinetic energy into potential energy through deformation energy, the higher he jumps.
Part of energy is of course transformed in other types of energy, for example internal energy of the pole, resulting in heat. In mechanics such ability is described by the quantity called power Mathematically this can be expressed as: Instantaneous power is work performed over time period that is approaching zero.