The moment of inertia of an electron in nth orbit will be MR (a) MR (b) 2 (d를 MR: (d) MR (d)를 MR,
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- A uranium ion and an iron ion are separated by a distance of R = 57.10 nm, as shown in the figure. The uranium atom is uranium ion iron ion electron singly ionized; the iron atom is doubly ionized. K r K- R Calculate the distance r from the uranium atom at which an electron will be in equilibrium. Ignore the gravitational r = nm attraction between the particles. What is the magnitude Fy of the force on the electron from the uranium ion? N Question Source: Freedman College Physics 3e | Publisher: MacmillanConsider an hydrogen-like atom with a very light particle of mass m rotating around a heavy particle of mass M which is much greater than m. The charge of the heavy particle is -e and the charge of the lighter particle is +3e. The light particle executes uniform circular motion about its center of rotation which is where the heavy particle is located. Assume that the centripetal acceleration of the lighter particle is due essentially only to the Coulomb force of attraction between the two particles. Given that the orbital angular momentum of the light particle around its center of rotation is L = mvr =ħ, where v is the lighter particle's speed and r is its distance from the center of rotation, determine the speed of the lighter particle relative to the heavy particle. ke² HINT: you might want to make use of the relation hc 1 Recall that: ħ = 1.06 x 10-34 J-s; k= 4π€0 137. = 9 x 10⁹ Nm²/C² and e = 1.6 × 10-19 C.An alpha particle (four times the mass of a proton with a charge of +2e) is moving at 3.0 x 105 m/s [E] very far away from a proton. The proton is moving directly towards the alpha particle at a velocity of 1.0 x 105 m/s [W]. Find the minimum possible distance between the two particles.
- +Q + a a (a) What is the dipole moment of the configuration shown above? If Q = 5.5 µC and a = 1.8 nm? Vi+ k C.m (b) What is the torque on this dipole with an electric field of 4.5×1051 N/C? 7 = √i+ [vi+ VkNm (c) What is the torque on this dipole with an electric field of -4.5×105 N/C? 7 = k Nm +Two equal point masses m₁ = m2 = 0.69 kg are attached to the ends of a rod of a negligible mass and length of ().81 m. The rod is placed at rest on the y axis and is free to move in a horizontal and frictionless table, as seen in the figure. m1 m3 νο m2 x A third point mass m3, identical to the two other masses, moves with velocity vo collides head-on with completely inelastically collision with m2. = 1.62 m/s to the right so that at t = () it a. Find the center of mass (XCM, YCM) of the three bodies at t₁ = 1.2 s after the collision: Хом 0.64 = Усм -0.2 X b. What is the magnitude of the angular momentum of the system relative to the origin of coordinates? 0.90 X c. What is the magnitude of the angular momentum of the system relative to the center of mass? 0.60 X d. What is the angular velocity of the rod after the collision? 0.5 X e. What is the linear velocity of the body m₁ right after the collision (relative to the laboratory frame of reference)? 0An electron has a mass of 9.11x10-31 kg. In the Bohr model of the hydrogen atom, the electron is viewed as orbiting the single proton in the nucleus; the centripetal force is provided by the electrical attraction between the oppositely charged proton and electron. The radius of orbit is 5.29x10-11 m. What is the speed at which the electron moves as it orbits the proton. (Hint: Centripetal acceleration is v2/r.) A) 2.28*106 m/s B) 5.33*104 m/s C) None of these.
- An electron is orbiting a nucleus which has a charge of 14e, under the action of the Coulomb force at a radius of 1.14 × 10-¹0 m. Calculate the angular velocity of the electron, in radians per second. @=||Which of the following relationships is not true of quantities associated with classical rotational dynamics? (L represents angular momentum, u is the reduced mass, w is angular velocity, and / is the moment of inertia) 1 E= L² 21 L=/w I= µr² L=T·PAn electron is emitted from an electron gun with an initial speed of 3.50 × 105 m/s. It collideselastically with a second electron which is initially at rest. Since these two electron have thesame charge, they exert a repulsive electrostatic force toward each other. After the collision,one electron moves off at an angle of 37.0° to the original direction of motion, and the seconddeflects at an angle of θ to the same axis. Calculate the final speeds of the two electrons andthe angle θ
- Water molecule is modeled as a dipole with an effective separation, d = 3.9×10-12 m between its positive and negative charges. The water molecule’s dipole moment is p = 6.2×10-30 C∙m. Consider water molecules in the lower atmosphere where the electric field has a magnitude of about 325 N/C. Assume the field is uniform. (a) What is the maximum torque exerted on a water molecule? (b) Find the change in potential energy if a water molecule rotates from j = 170o to j = 180o?r -e Physical constants (A) What is the radius of the orbit with n = 4? (B) What is the speed of the orbit with n = 4? The old Bohr model of the hydrogen atom was based on... (1) the assumption that the electron travels on a circle h = 6.626 x 10-34 Js; -28 (A) (in m) Bohr Model mv² r mvr = n and obeys Newton's second law, and (2) the hypothsis that angular momentum is quantized. For the Bohr model, Ke² = 2.307 x 107 Jm; 31 m9.11 x 10 kg. (B) (in m/s) Ke² 12. (1) (2) OA: 2.034x10-10 OB: 2.706x10-10OC: 3.598x10-10 OD: 4.786x10-10 OE: 6.365x10-10 OF: 8.466x10-10 OG: 1.126x109 OH: 1.497x109 OA: 8.533x104 OB: 1.237x105 OC: 1.794x105 OD: 2.601x105 OE: 3.772x105 OF: 5.470x105 OG: 7.931x105 OH: 1.150x106A pith ball is a small foamy ball that can carry an electriccharge. A pith ball with a mass of 5.00 mg carries a chargeof 3.00μC. It is on the end of a 10.0 cm string. The pithball is orbiting around a fixed object in a horizontal circle.If the pith ball orbits with a tangential speed of 2.00 m/sat a distance of 5.00 cm from the fixed charge, what it themagnitude of the fixed charge being orbited? The stringmakes an angle of 30° with the vertical.