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.

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

An electron (mass m=9.11×10−31kgm=9.11×10−31kg) is accelerated from the rest in the uniform field E⃗ E→ (E=1.45×104N/C)(E=1.45×104N/C) between two thin parallel charged plates. The separation of the plates is 1.10 cm. The electron is accelerated from rest near the negative plate and passes through a tiny hole in the positive plate. Show that the gravitational force can be ignored.

Two point charges of mass m each are suspended in the gravitational field of the Earth by two non-conducting massless strings, each of length 1, attached to the same fixed point. The spheres are given equal charges Q of the same sign. As a result each string makes angle a to the vertical (see figure below). Write down an expression for the tension of a string T in terms of Coulomb force Fc between the charges and the angle a. Use the following notation (without the quotes): "/" for division, "*" for multiplication, "+" an "_" as usual. For powers used "^2", while for square root use "sqrt". To indicate that square root applies to the whole expression use brackets - for example, for √AB use sqrt(A*B). For Greek letters such as л, α etc. use pi, alpha. For example to get 14√AB use 1/pi*A^2/B*sqrt(AB). Please use the exact variables given in the conditions of the problem: e.g if L is given, then do not use 1. For subscripts such as Fc simply write "FC" (without the quotes). Please use…