Review a magnetic dipole moment model made of the motion of electrons orbiting the nucleus of an atom. An electron orbits the nucleus of a Hydrogen atom with the radius of the orbit of the R circle and the orbit is in the xy plane. If one electron and proton are m, and m, mass respectively (m, » m,) and charged -e and e, Determine the angular velocity of the movement of electrons orbiting electrons
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- In 1911, Ernest Rutherford and his assistants Geiger and Marsden conducted an experiment in which they scattered alpha particles (nuclei of helium atoms) from thin sheets of gold. An alpha particle, having charge +2e and mass 6.64 x 10-2 kg, is a product of certain radioactive decays. The results of the experiment led Rutherford to the idea that most of an atom's mass is in a very small nucleus, with electrons in orbit around it. Assume an alpha particle, initially very far from a stationary gold nucleus, is fired with a velocity of 1.41 x 107 m/s directly toward the nucleus (charge +79e). What is the smallest distance between the alpha particle and the nucleus before the alpha particle reverses direction? Assume the gold nucleus remains stationary. fmIn 1911, Ernest Rutherford and his assistants Geiger and Marsden conducted an experiment in which they scattered alpha particles (nuclei of helium atoms) from thin sheets of gold. An alpha particle, having charge +2e and mass 6.64 x 10-27 kg, is a product of certain radioactive decays. The results of the experiment led Rutherford to the idea that most of an atom's mass is in a very small nucleus, with electrons in orbit around it. Assume an alpha particle, initially very far from a stationary gold nucleus, is fired with a velocity of 2.98 × 107 m/s directly toward the nucleus (charge +79e). What is the smallest distance between the alpha particle and the nucleus before the alpha particle reverses direction? Assume the gold nucleus remains stationary. fmIn 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
- Three identical particles have the same mass m and the same positive charge Q. They are initially at rest at the corners of an equilateral triangle with side a when one is released while the other charges are held fixed. What is the speed of the moving charge when it is a large distance from the others?What is the total energy stored in the following 3-charge system? 2 nC + 2 cm 2 cm -1 nC Ο 22.5 μ Ο 1.8 μ O -0.45 μJ O 0.45 W Ο -22.5 μ 2 cm + 1 nCA hydrogen atom contains a single electron that moves in a circular orbit about a single proton. Assume the proton is stationary, and the electron has a speed of 7.6 105 m/s. Find the radius between the stationary proton and the electron orbit within the hydrogen atom.
- L vo y E A uniform field E = -150000j N/C exists between two plates of length L = 3 cm, as shown in the figure above. A proton is fired at an angle of 40° to the x axis with an initial speed of 7300000 m/s. a) Find its vertical coordinates as it emerges from the plate, assuming the proton will not hit any plate in the process. cm b) Find the angle at which it emerges. degrees to the x axis.Multiple-Concept Example 3 provides some pertinent background for this problem. Suppose a single electron orbits about a nucleus containing two protons (+2e), as would be the case for a helium atom from which one of the naturally occurring electrons is removed. The radius of the orbit is 2.92 × 10-¹¹ m. Determine the magnitude of the electron's centripetal acceleration. Number UnitsFour electrons are orbiting a stationary proton along a perfect circle with a constant speed v as shown below. Find the orbital speed and frequency of this circular motion if the radius of the orbit is 0.4. 10-¹0m. The elementary charge q = 1.6 · 10-¹⁹C and the electron mass m₂ = 9.11 · 10−³¹ kg. -31 V - q • q -q V The orbital speed, v = 2.51E6 x Units m/s - q The frequency of orbital motion, f 9.99E15 x Units Hz ✓✓.
- Multiple-Concept Example 3 provides some pertinent background for this problem. Suppose a single electron orbits about a nucleus containing two protons (+2e), as would be the case for a helium atom from which one of the naturally occurring electrons is removed. The radius of the orbit is 3.08 × 10-¹¹ m. Determine the magnitude of the electron's centripetal acceleration.Calculate the angular velocity ω of an electron orbiting a proton in an atom, assuming the radius of the orbit is 5.02×10^-11 m. You may assume that the proton is stationary and the centripetal force is supplied by Coulomb attraction.A thin metal ring of radius R is placed horizontally and charged with charge Q. A point like object with mass m and charge q is let fall vertically from a height H measured from the plane of the ring. The initial velocity is zero. The object is falling along the axis of a ring. What is the velocity of the object, when it reaches the middle of the ring? Gravitational acceleration is denoted by g.