Consider 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 = mur = 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. HINT: you might want to make use of the relation ² = 137. ke² he Recall that: ħ = 1.06 x 10-34 J-s; k=1=9x 109 Nm²/C² and e = 1.6 x 10-19 C. 4reo

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: 1.150x106

A 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.

In the classic model of the hydrogen atom proposed by Niels Bohr, the electron rotates around a stationary proton in a circular orbit with an approximate radius r = 0.053 nm, see the figure below. (a) Find the magnitude of the electrostatic force of attraction, Fe, between the electron and the proton. (b) Find the magnitude of the gravitational force of attraction, Fg, between the electron and the proton, and then find the Fe / Fg ratio.

In a hydrogen atom an electron is orbiting a proton. There are two forces between the electron and the proton. The Gravitational Force FG and the electrostatic Force FE.  What is the factor   FE / FG   of those two forces.    Use the following constants to calculate the problem:  me=9.1*10-31 kg mp=1.67*10-27 kg e=1.6*10-19 C k=8.99*109 Nm2/C2 r=1.11*10-10 m   ?=6.67⋅10−11??2??2G=6.67⋅10−11Nm2kg2 Please give your answer FE/FG in FE/FG*1040 ie. for 6.734*1042  please write  673.4

The proton-proton chain is the multi-step process that powers the Sun via fusion of hydrogen into helium. In the first step of the proton-proton chain, a positron is produced when two protons fuse together (with one proton converting to a neutron). The emitted positron quickly collides with its anti-particle, the electron. (Recall that the electron and positron have exactly the same mass, but opposite electric charges.) The electron and positron then completely annihilate, converting all of their rest mass into two gamma-ray photons. Given a single particle of mass m, the amount of energy E produced when all of its mass is converted to energy is given by Einstein's famous formula, E = m c?, where c = 2.9979 x 10° m/s is %3D the speed of light. We also learned that the energy Ephoton of a single photon is related to its frequency f or wavelength A via Ephoton = hf = hc where h = 6.626 x 1034 m² kg/s is a fundamental constant of nature called Planck's constant. In the electron + positron…

Consider the two charges in the figure, which are moving in opposite directions and located a distance 11 cm on either side of the origin of the given coordinate system. Charge one is 19.5 uC and is moving at a speed 19.5 x U2 10° m/s, and charge two is -8.5 µC and is moving at a speed of 6.5 x 106 m/s. Notice that the positive z-direction in this figure is directed out of the page. 92 d What is the total magnetic field, in the z-direction, at a point Q located a distance 45 cm down the x-axis, as shown? d 91

In the early 1900s, scientists modelled the hydrogen atom as an electron orbiting a proton. Like when we look at the Earth and Sun, we can consider the proton to be stationary, and the electron to be in orbit around the proton in a perfect circle. Unlike the Earth and Sun, the force responsible for the circular motion of the electron is the attractive electric force between the proton and electron. All other forces can be ignored. Experiments showed that the electron's orbital radius was 5.29x10^-11m. a) Calculate the speed of the electron in its orbit. b) Show that the circumference of the electron's orbit (2 times pi times radius) is about equal to the electron's De Broglie wavelength at that speed. Electron: mass = 9.11x10^-31kg, charge = -1.60x10^-19C. Proton: mass = 1.67x10^-27kg, charge = +1.60x10^-19C. Coulomb's constant: k = 9.00x10^9 Nm^2/C^2 Planck's constant: h = 6.63x10^-34 Js

Considering electron and proton as two charged particles separated by d = 4.5 x 10m calculate the gravitational force between the proton and electron and find its ratio to the Coulomb force. Take the mass of the proton 1.7 x 10-27 kg, the mass of the electron 9.1 x 10-³1 kg, the value of 1 the universal gravitational constant 6.7 × 10-¹1 N kg-2m-2, the electron charge -1.6 × 10- C and = 9 x 10⁹ m/F. Give the answer for Απερ the gravitational force in 10-47 N. 19

In an experiment similar to the setup described in the Example, a positively charged particle of mass m is released from rest at the surface of the positive plate. The velocity of the particle at the negative plate is 1.30 ✕ 105 m/s. If the electric field magnitude is 6.00 ✕ 103 N/C, the distance between the two plates is 5 cm, and the charge on the particle is 3e, what is the particle's mass (in kg)?