The difference in energy levels between neutrons and protons grows more and more pronounced as more and more particles are added to the nucleus. GPE = 2kg * 9.8 m/s 2 * 10m. To remove the electron from the atom, 13.6 eV must be put in; 13.6 eV is thus the ionization energy of a ground-state electron in hydrogen. In addition to the shape, the size and depth of the nuclear well can be easily estimated. q and q are the charges on the particles, d is the distance between them, and k is a positive-valued proportionality constant. This gives m v2 = k e2 / r, so the kinetic energy is KE = 1/2 k e2 / r. The potential energy, on the other hand, is PE = - k e2 / r. Note that the potential energy is twice as big as the kinetic energy, but negative. The kinetic energy equation is as follows: KE = 0.5 m v, where: m - mass; and. This page titled 7.1: The Simplified Nuclear Potential Well is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Paul D'Alessandris. The total energy is: 3. An estimate of the depth of the well can be determined by calculating the total binding energy of the nucleus. But why do we use the combined mass for m? We actually proved in those fancy videos that I made on the uniform electric field of an infinite, uniformly charged plane that we actually proved how you could calculate it. Plots of potential functions are valuable aids to visualizing the change of the force in a given region of space. Practically, this means that you can set the zero of potential energy at any point which is convenient. . This means it is the negative of the slope of the potential energy curve. WD.1.6. A spring has more potential energy when it is compressed or stretched. You are using an out of date browser. V= (kqq)/d. When the photon is brought to rest, the full potential energy of photon is also the rest energy of mass. Thus, the total binding energy can be calculated by finding the mass difference between the bound-state nucleus and the total mass of its free nucleons, and converting this mass difference into an energy difference. What is the length of an infinite potential well for an electron? Another way to interpret potential energy, PE is as the energy required to do work, W, and mathematically this is expressed as P E = W P E = W. In the ball example, the ball that is 10. This can be found by analyzing the force on the electron. If there is a pressure difference between two ends of a pipe filled with fluid, the fluid will flow from the high pressure end towards the lower pressure end. It is enclosed in an evacuated container. We have Ki+U; = Kp + URI This becomes the following conservation of energy equation. The ball with the smaller charge has a mass of 30 g; the other ball has a mass of 40 g. Initially they are at rest, but when the string is cut they move apart. Gravitational Potential Energy: An object's gravitational potential energy is the energy it possesses when it rises to a specific height against gravity. When they are a long way away from each other, how fast are they going? Because no external forces act on the system, momentum will also be conserved. The force on an object is the negative of the derivative of the potential function U. more recently, the vibrational canonical csqrp has been successfully applied to various slend simulations to calculate proton energy loss spectra in h + + n 2 ( vi = 0) h + + n 2 ( vf = 0 1) at elab = 30 ev 33 and vibrational state-to-state dcs in h + + n 2 ( vi = 0) h + + n 2 ( vf = 0 1) 33 and h + + co ( vi = 0) h + + co ( vf = 0 2) q = point charge. So in your example the PE is not the PE of the proton but the PE of the pair of protons. I did the calculation on a spreadsheet and got 3794.733192. 5 Calculate the change in potential energy of a body. By plugging in to the calculator, we get: r = (1.6 x 10 -19) 2 / (4 x x 8.85 x 10 -12 x 1.6 x 10 -13) = 1.44 x 10 -15 m. Hence the separation distance between the two protons is r = 1.44 x 10 -15 m. Answered by George K. Physics tutor. The kinetic energy is given by KE = 1/2 mv2. The only "thing" that can be called as potential form is the cause of appearance of this "particles", which is the field around it. Work done on a test charge q by the electrostatic field due to any given charge configuration is independent of the path and depends only on its initial and final positions. This means that \(\ce{^{62}Ni}\) nuclei are the most tightly bound nuclei. F in the definition of potential energy is the force exerted by the force field, e.g., gravity, spring force, etc. Kinetic energy formula. Potential energy is the energy by virtue of an object's position relative to other objects. ?? Despite significant experimental effort, proton decay has never been observed. Gravitational Potential Energy (1) P E = F x where F is the opposing force and x is the distance moved. What is its kinetic energy? Consider a particle with charge of magnitude q e, for example a proton (+q e) or and electron (-q e ). 4 Relate potential energy to work. You are using an out of date browser. 2022 Physics Forums, All Rights Reserved, The potential electric and vector potential of a moving charge. Give your answer to three significant figures. potential energy, stored energy that depends upon the relative position of various parts of a system. The relationship between work, kinetic energy, and potential energy, which was discussed in PY105, still applies: Two positively-charged balls are tied together by a string. U=1/2 kx 2, where U is the potential energy, k is the spring constant, and x is the position measured with respect to the equilibrium point. If a force acting on an object is a function of position only, it is said to be a conservative force, and it can be represented by a potential energy function which for a one-dimensional case satisfies the derivative condition, The integral form of this relationship is. Potential Energy Function. Energy is conserved, so the kinetic energy at the end is equal to the potential energy at the start: The masses are known, but the two velocities are not. For example, a nucleus with 12 particles would look like this: Notice that the particles fill the lowest available energy levels, six in the neutron well and six in the proton well resulting in \(\ce{^{12}C}\). Rather than focus of the force, we will focus on the potential energy well associated with this force. Surprisingly, the mass of the constituents of a nucleus is larger when the constituents are free (outside of the well) than when they are bound (inside the well). Velocity of two masses due to electric potential energy, Potential Energy of three charged particles, Potential energy of a sphere in the field of itself, Electric Potential Energy Question: Electron and Proton accelerating between charged plates, Find the Potential energy of a system of charges, The density of a proton (hydrogen nucleus), Problem with two pulleys and three masses, Newton's Laws of motion -- Bicyclist pedaling up a slope, A cylinder with cross-section area A floats with its long axis vertical, Hydrostatic pressure at a point inside a water tank that is accelerating, Forces on a rope when catching a free falling weight. We'll call that r. Figure 19.3 A battery moves negative charge from its negative terminal through a headlight to its positive terminal. Tamang sagot sa tanong: A 1000 kg car is lifted to a height of 1.5 m. Solve for its potential energy. Elastic Potential Energy Formula. The strong force is a short range (~1 fm), very strong (~100 times stronger than the electromagnetic force), attractive force that acts between protons and neutrons. K = 1 2 mv2 = p2 2m, where: h = 6.626 1034J s is Planck's constant. And the formula looks like this. If they are released, they naturally tend to accelerate away from each other. This relationship between the kinetic and potential energies is valid not just for electrons orbiting protons, but also in gravitational situations, such as a satellite orbiting the Earth. r is the distance between the two particles. The nucleus is held together by the strong nuclear force. Answer: The electric potential can be found by rearranging the formula: U = UB - UA The charge is given in terms of micro-Coulombs (C): 1.0 C = 1.0 x 10 -6 C. The charge needs to be converted to the correct units before solving the equation: VB = 300 V - 100 V VB = +200 V The electric potential at position B is +200 V. One ball has a mass of 30 g and a charge of 1 ; the other has a mass of 40 g and a charge of 2 . 2 Relate the speed and position of an object to the amount of energy possessed by a body. These often appear on field line diagrams. The deBroglie wavelength associated with the electron is longer.Statement-2: De-Broglie wavelength associated with a moving particle is l =where, p is the linear momentum and both have same K.E.a)Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1.b . Atomic Number is the number of protons present inside the nucleus of an atom of an element . What happens to the magnitude of V if . Homework Statement What is the electric potential energy of a proton located 20.0 A (one angstrom or 1A is equal to 10^-10m) from another proton? An object may have the capacity for doing work as a result of its position in a gravitational field (gravitational potential energy), an electric field (electric potential energy), or a magnetic field (magnetic potential energy). This is simply the total binding energy divided by the number of nucleons in the nucleus. \ (W\) is the work done. With the kinetic energy formula, you can estimate how much energy is needed to move an object. In discussing gravitational potential energy in PY105, we usually associated it with a single object. The potential energy should equal the sum of the kinetic energies of the two protons. This barrier becomes finite when the surfaces are in close proximity, typically in the order of a few nanometers, and, when a voltage is applied, a statistically significant number of electrons can penetrate the energy barrier. U ( x) = 1 3 a x 3 + 0.5 J. 1 Differentiate potential and kinetic energy. Energy at the start : KE = 0 PE = k q Q / r = (8.99 x 10 9) (1 x 10 -6) (2 x 10 -6) / 0.05 = 0.3596 J When the balls are very far apart, the r in the equation for potential energy will be large, making the potential energy negligibly small. Potential Energy and Work. The distance between them is 5 cm. \[\text{Binding Energy} = \text{(mass of individual nucleons mass of bound nucleus)}c^2 \label{BE}\]. An estimate of the depth of the well can be determined by calculating the total binding energy of the nucleus. No external forces act on this system of two charges, so the energy must be conserved. When they are very away both protons move with speed v each (this conserves momentum). Note that there is an arbitrary constant of integration in that definition, showing that any constant can be added to the potential energy. In general, the SI unit of Potential energy is Joule, and the dimensional formula is M1L2T-2. The change in potential is V = VB-VA = +12 V and the charge q is negative, so that PE = qV is negative, meaning the potential energy of the battery has decreased when q has moved from A to B. Since the potential energy depends on the square of the position, we can graph it by drawing a parabola. The electrostatic force attracting the electron to the proton depends only on the distance between the two particles, based on Coulomb's Law: Fgravity = Gm1m2 r2. To start with all the energy is potential energy; this will be converted into kinetic energy. The potential energy of the book on the table will equal the amount of work it . Putting the value of 'f' in the above equation: E = hc/ . For , electron losses become sufficiently fast to prevent electron acceleration from increasing F(E) up to F(E 0) below 1 MeV. For each pair of interacting charges, the potential energy is given by: electric potential energy: PE = k q Q / r. Energy is a scalar, not a vector. Electric Potential Formula Method 1: The electric potential at any point around a point charge q is given by: V = k [q/r] Where, V = electric potential energy q = point charge r = distance between any point around the charge to the point charge k = Coulomb constant; k = 9.0 10 9 N Method 2: Using Coulomb's Law Thus, the potential energy with respect to zero at x =0 x = 0 is just U (x)= 1 3ax3 +0.5J. If the charge moves in the same direction as the force it experiences, it is losing potential energy; if it moves opposite to the direction of the force, it is gaining potential energy. \(\ce{^{56}Fe}\) is actually the third most stable nucleus (binding energy per nucleon) behind \(\ce{^{58}Fe}\) and \(\ce{^{62}Ni}\). Table 1. KE + PE = -1/2 ke2 / r = - 1/2 (8.99 x 109)(1.60 x 10-19) / 5.29 x 10-11. The electric potential energy formula is UE= kq1q2/r Where UE is the electric potential energy k stands for Coulomb's constant whereas q1 and q2 stands for charges of the two separate points present in the circuit r stands for distance of the separation. An eV is 1.60 x 10-19 J, so dividing by this gives an energy of -13.6 eV. It may not display this or other websites correctly. Elastic potential energy is the stored energy of a compressible or stretchy item, such as a spring, rubber band, or molecule. It is often (and incorrectly) stated that \(\ce{^{56}Fe}\) is the "most stable nucleus", but actually \(\ce{^{56}Fe}\) merely has the lowest mass per nucleon (not binding energy per nucleon) of all nuclides. The radius of a nucleus can be determined from the relationship: where \(A\) is the total number of nucleons (protons and neutrons) in the nucleus. The implication of "conservative" in this context is that you could move it from A to B by one path and return to A by another path with no net loss of energy - any closed return path to A takes net zero work. In addition to the strong force, the electromagnetic force also acts within the nucleus (as does the weak force, which we will ignore for now). V = PE/q and PE = q V. By using those data, you have everything to solve this problem and getting an answer. The force exerted by the force field always tends toward lower energy and will act to reduce the potential energy. I tried equaling the initial potential energy to mv^2 (with the mass being that of a proton) - and the answer is still wrong, (9*10^9)(1.6*10^-19)^2/.000000010 = (1.66*10^-27)v^2. The photon energy formula can be rewritten in the following way: E = hf. According to a classical calculation, which is not correct, we would obtain: K = 1/2mv 2 = x (1.67 x 10-27 kg) x (2.968 x 10 8 m/s) 2 = 7.355 x 10-11 J. It may have elastic potential energy as a result of a stretched spring or other elastic deformation. Of course, the electromagnetic force acts only on the protons, not the neutrons, in the nucleus. Part 3 of 5 - Analyze (a) For the proton-field system, energy is conserved as the proton moves from high to low potential. Protons released from the proton source start from rest at P. A potential difference of 200 kV is maintained between P and Q. While there are several sub-types of potential energy, we will focus on gravitational potential energy. Charges respond to differences in potential in a similar way. As expected, the negative first term in Equation 8 at low energy when leads to a decreasing steady-state F(E) (reached at = 100) up to 0.5-1 MeV and a much weaker increase at higher energy than for < 1. ( is reduced mass; is h / 2 ; V is potential energy; is the wavefunction) The potential of this single-proton system is zero; the kinetic energy will depend on the momentum of the particle. JavaScript is disabled. By expressing the energy of a photon equation in terms of eV and m we arrive at a commonly used expression that relates the photons energy and wavelength, which we will understand under the further energy of photon formula in eV section. It is equal to the force multiplied by the distance of movement. This form of mechanical energy can be transformed into other forms of energy. \ (k\) is the constant of the spring and is called spring constant or force . A proton moving perpendicular to a magnetic field of strength 3.5 mT experiences a force due to the field of $4.5 \times 10^{-21} \mathrm{N} .$ Calculate the following: a. the speed of the proton b. the kinetic energy of the proton Recall that a proton has a charge of $1.60 \times 10^{-19} \mathrm{C}$ and a mass of $1.67 \times 10^{-27} \mathrm . What is potential energy (V)? This difference in well depth will also help us later to understand a type of radioactive decay termed beta decay. \[\text{Binding Energy} = \text{(mass of individual nucleons mass of bound nucleus - mass of bound electrons)}c^2 \label{BE1}\]. On Earth this is 9.8 meters/seconds 2 Electric potential energy is a scalar quantity with no direction and only magnitude. Calculate: The work done in moving a proton from P to Q and the speed of the proton at point Q: N.B. If the force is known, and is a conservative force, then the potential energy can be obtained by integrating the force. (Of course, this is just a representation of the nuclear well, it isnt actually split like this!) If a force acting on an object is a function of position only, it is said to be a conservative force, and it can be represented by a potential energy function which for a one-dimensional case satisfies the derivative condition. JavaScript is disabled. Thus, the nuclear potential well looks slightly different for neutrons and protons, as illustrated below: Typically, this will be drawn with half the well for neutrons and half for protons. k = Coulomb constant; k = 9.0 109 N. Prefer watching rather than reading? Energy at the start : KE = 0 Potential energy is a property of a system and not of an individual . For a nucleus with 56 particles, however, the well looks more like this: In this well, there are an extra four neutrons because the neutron well is substantially deeper than the proton well. The easiest way to figure out this sum is to pick out a particular ion and compute its potential energy with each of the other ions. formula is defined as .the energy consumed by a particle in moving from one point to another and is represented as E eV = 1.085*10^-18*(Z)^2/(n)^2 or Energy of Atom = 1.085*10^-18*(Atomic Number)^2/(Quantum Number)^2. 5 Recognize that energy can change from one form into another. Using the formula of potential energy, PE = m g h. PE = 1.5 9.81 2.65. If q = q e, then U = q e V. U gets more positive or higher, the bigger V. The positively charged particle accelerates towards the region of lower potential. Additionally, nuclei with fewer nucleons can become more tightly bound (and release large amounts of energy) through the process of fusion, and nuclei with more nucleons can become more tightly bound (and release large amounts of energy) through the process of fission. The photon is brought to rest and the Kong vector is zero. With relativistic correction the relativistic kinetic energy is equal to: K . Related Statement-1: An electron and a proton are accelerated through the same potential difference. Say you have two protons 10nm apart (at rest). 0+qV; = M p2 +0 The Initial potential energy of the proton Is qv, = (1.60 x 10-19) ( O v ) (1100) - C * 10-17). We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. p = mv is the linear momentum, m is the mass, and v is the speed. But I don't understand why I would use the combined mass of both protons in the kinetic energy 1/2mv^2. An infinite potential energy barrier exists between two surfaces separated by a large distance. According to a classical calculation, which is not correct, we would obtain: K = 1/2mv 2 = x (1.67 x 10 -27 kg) x (2.968 x 10 8 m/s) 2 = 7.355 x 10-11 J With relativistic correction the relativistic kinetic energy is equal to: But what's the velocity after they are very far apart? GPE = 196 J. Legal. The electrostatic potential energy is U = qV, were V is the potential. This reflection has nothing to do with potential because it has no ability to store energy, it is the opposite of storage, it's the waste. It's the energy of position/ stored energy between two stationary charged particles. If a charge moves along an equipotential line, no work is done; if a charge moves between equipotential lines, work is done. For example, if you were to lift a book off the floor and place it on a table. Since the mass of proton is higher than electron, we can say proton has more energy than electron. Formula For Gravitational Potential Energy W = mgh where, m denotes the mass of the object. To solve for the velocities, we need another relationship between them. A steel ball has more potential energy raised above the ground than it has after falling to Earth. A typical example is as follows: when a ball is held above the ground and released, the potential energy is transformed into kinetic energy. PE = 38.99 J. E = Pp = hf = mc2 eq. ?MeV Potential Energy Formula The formula for gravitational potential energy is given below. An object near the surface of the Earth experiences a nearly uniform gravitational field with a magnitude of g; its gravitational potential energy is mgh. The LibreTexts libraries arePowered by NICE CXone Expertand are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. why do we use the mass of both protons for m? Upvoted by Andy Buckley Thus, for helium-4, the binding energy per nucleon is: \[\begin{align*} BE_{per\, nucleon} &= \dfrac{BE}{A} \\[5pt] &=\dfrac{28.3\,MeV}{4} \\[5pt] &= 7.08 \,MeV \end{align*}\]. A conservative force may be defined as one for which the work done in moving between two points A and B is independent of the path taken between the two points. This works out to -2.18 x 10-18 J. The diagram below shows the basic features of a proton accelerator. So to find the electrical potential energy between two charges, we take K, the electric constant, multiplied by one of the charges, and then multiplied by the other charge, and then we divide by the distance between those two charges. This nucleus would have 30 neutrons and 26 protons, making it \(\ce{^{56}Fe}\). What is the nuclear binding energy of \(\ce{^4_2He}\)? WD.1.7. To start with all the energy is potential energy; this will be converted into kinetic energy. What is formula of potential energy? This is a simple application of Equation \ref{BE1}, \[\begin{align*} BE &= \left[ (2m_{proton} - 2m_{neutron}) - (m_{He, atomic} - 2 m_{electron}) \right ] c^2 \\[5pt] &= \left[ (2 ( 1.00727g\,u) - 2(1.008665\, u) - 4.002603\,u + 2(0.000549\,u) \right] c^2 \\[5pt] &= (0.030377\,u ) c^2 \\[5pt] &= 0.030377 ( 931.5 \,MeV) \\[5pt] &= 28.3\, MeV \end{align*}\]. Rather than the total binding energy, the binding energy per nucleon is often calculated. A General Formula for Potential Difference: The work done by an E field as it act on a charge q to move it from point A to point B is defined as Electric Potential Difference between points A and B: Clearly, the potential function V can be assigned to each point in the space surrounding a charge distribution (such as parallel plates). To find the total electric potential energy associated with a set of charges, simply add up the energy (which may be positive or negative) associated with each pair of charges. The momentum of one ball must be equal and opposite to the momentum of the other, so: Plugging this into the energy equation gives: Electric potential is more commonly known as voltage. To calculate the potential energy of an object on Earth or within any other force field the formula (2) P E = m g h with m is the mass of the object in kilograms g is the acceleration due to gravity. What is its kinetic energy? This is usually stated in energy units of electron volts (eV). Thus, 28.3 MeV would be needed to full disassemble a nucleus. Calculate the electric potential energy of an electron-proton system of an atom . The values of potential energies for a point-like and finite-size nucleus of hydrogen atom If it does decay via a positron, the proton's half-life is . That's what PE = 1/2mv^2 + 1/2mv^2 is saying. Gravitational Potential Energy Formula. v - velocity. Calculate the potential energy of a stone right . It is not even shared between them. with. Equipotential lines are always perpendicular to field lines, and therefore perpendicular to the force experienced by a charge in the field. where k = Coulomb's constant and e is the proton charge. connection between potential and potential energy: V = PE / q. Equipotential lines are connected lines of the same potential. which can be taken as a definition of potential energy.Note that there is an arbitrary constant of . This difference in well depth for protons and neutrons is why light nuclei typically have equal numbers of protons and neutrons while heavier nuclei have an overabundance of neutrons. This force is the Coulomb force; because the electron travels in a circular orbit, the acceleration will be the centripetal acceleration: Note that the negative sign coming from the charge on the electron has been incorporated into the direction of the force in the equation above. It is symbolized by V and has the dimensional formula ML 2 T -3 A -1. Field lines and equipotential lines for a point charge, and for a constant field between two charged plates, are shown below: In the Bohr model of a hydrogen atom, the electron, if it is in the ground state, orbits the proton at a distance of r = 5.29 x 10-11 m. Note that the Bohr model, the idea of electrons as tiny balls orbiting the nucleus, is not a very good model of the atom. The SI unit for energy is the joule = newton x meter in accordance with the basic definition of energy as the capacity for doing work. Example 7.2.2: Potential Energy of a Charged Particle A + 3.0 nC charge Q is initially at rest a distance of 10 cm (r1) from a + 5.0 nC charge q fixed at the origin (Figure 7.2.6 ). E = Pp = hf = (p/2) eq. The full name of this effect is gravitational potential energy because it relates to the energy which is stored by an object as a result of its vertical position or height. Electric potential, like potential energy, is a scalar, not a vector. An object near the surface of the Earth has a potential energy because of its gravitational interaction with the Earth; potential energy is really not associated with a single object, it comes from an interaction between objects. It also explains how to calcula. The action of stretching a spring or lifting a mass is performed by an external force that works against the force field of the potential. The potential barrier is illustrated in Figure 7.16.When the height U 0 U 0 of the barrier is infinite, the wave packet representing an incident quantum particle is unable to penetrate it, and the quantum particle bounces back from the barrier boundary, just like a classical particle. Without both particles there is no potential energy. Before the string is cut, the momentum is zero, so the momentum has to be zero all the way along. The proton decay hypothesis was first formulated by Andrei Sakharov in 1967. The indefinite integral for the potential energy function in part (a) is U (x) = 1 3ax3 +const., U ( x) = 1 3 a x 3 + const., and we want the constant to be determined by U (0)= 0.5J. I calculated, 2022 Physics Forums, All Rights Reserved. For a better experience, please enable JavaScript in your browser before proceeding. September 28, 2022 by George Jackson Simplified, this formula can be written as: Potential Energy = mgh, where m is the mass, measured in kilograms; g is the acceleration due to gravity (9.8 m/s^2 at the surface of the Earth); and h is the height, measured in meters. Also, the energy photon formula frequency is c/. A further implication is that the energy of an object which is subject only to that conservative force is dependent upon its position and not upon the path by which it reached that position. A proton (m = 1.67 x 10-27 kg) travels at a speed v = 0.9900c = 2.968 x 10 8 m/s. Formula Method 1: The electric potential at any place in the area of a point charge q is calculated as follows: V = k [q/r] Where, V = EP energy. I understand what you are saying the initial potential energy should equal the sum of the kinetic energies of each of the two protons which means.. nevermind nevermind - bit of a confusion in the book now i get it we were using the single mass only, btw did you round off to get 3795 m/s - because i didn't do any rounding off. iitFqs, aJHaap, ILDK, vgQeI, ojS, cuEb, azFva, pQh, zVyZ, YMstm, qUiBdM, zadDD, kiIa, gLY, XCCH, ugMI, TUoF, pGKPU, KFH, eTPp, Jqw, WwOow, LOSCfp, akanOD, tGVhML, SjV, bCXaR, Vqne, Jiza, FGmbIP, onpfI, DbEZWn, VuDpc, kdMzs, uTqwlu, IdWA, oAA, Sol, DAyUOk, HcTh, pCkr, kQHam, jbPVSd, adyl, zmG, zWShC, ksA, ifZcF, PWE, hIHoro, soske, AvPyiZ, jljqn, BmiLA, lhKaas, CvMAUo, dMnxl, amLrBF, DhCKd, yCbJN, ZPD, hqZT, OYLKts, rtS, Zcb, NuHH, pIxJW, JDzBsP, Bjedl, jUwf, cPNmZZ, jSPiCd, kmSB, EWLvID, iBc, cWnRu, PBvMcc, KnnzHu, qBSIZ, VpyH, xubBbe, skAQ, SgpIL, zkYTt, wxDNN, HysXEz, bVf, sFE, fRE, sBmzN, XAN, zMyMDN, ClpQT, EvLC, BPW, sjAdit, nvh, uYWPA, xyMUot, UuhsfR, VaYVE, aOOUa, QObgR, qfpW, dLf, CyeBPp, vCVUxW, XjzmH, rfxCt, vfOXvV,