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- Assume that an atomic nucleus can be thought of as a three-dimensional box with a width of 2 x 10^-14 m. If a proton moving as particles in this box, specify : The energy of the base state of the proton in MeVThe Van der Waals interaction energy between two spherical nanoparticles of diameters D₁ and D2, a distance d apart is found to be 1 f E -- A y y 12x²+xy+x x²+xy+x+y + Solid 1 D₁ Where A is a positive constant termed Hamaker constant and x = d +2ln Liquid x²+xy+x x²+xy+x+yl = d / D₁ and y = D₂ / D₁ Solid 2 D₂ Use the above expression to determine (a) the interaction energy of a sphere and an infinite flat surface and (b) the force between two identical spheres.5. (a) Derive the Larmour radiation formula for an accelerated point charge moving with non-relativistic velocity. (b) An electron is accelerated to 20 keV energy between anode and cathode separated by a distance of 5 cm. Calculate the total energy lost in radiation. 6+4
- (a) Show that the spread of velocities caused by the uncertainty principle does not have measurable consequences for macroscopic objects (objects that are large compared with atoms) by considering a 100-g racquetball confined to a room 15 m on a side. Assume the ball is moving at 2.0 m/s along the x axis.given oil density 900kg/m^3 fe=fg distance between capacitor plates d= 3.0 mm triangleV between plates= 15.0 v dropplet radious is 550nm in m is 5.5e-7 find charge on droplet q, number of electrons q/e, rounded # of electrons n & percent error charge q=mg/E , e=-1.60*10^-19c, %error-=|q/e-n|/n *1005. (a) Derive the Larmour radiation formula for an accelerated point charge moving with non-relativistic velocity. (b) An electron is accelerated to 20 keV energy between anode and cathode separated by a distance of 5 cm. Calculate the total energy lost in radiation.
- Protons of energy 5.1 MeV are incident on a silver foil of thickness 3.6 x 10-6 m. What fraction of the incident protons is scattered at the following angles? (The density of silver is 10.5 g/cm³, and its molar mass is 107.9 g/mol. Give your answer in decimal notation, e.g., 0.05 for 1/20.) (a) greater than 90° 3.716E-5 X (b) less than 5⁰Please explain why decreasing the total energy of the system make atoms more likely to stick togetherIn an experiment done by scattering 5.5-MeV ∝ particles from a thin gold foil, students fi nd that 10,000∝ particles are scattered at an angle greater than 50°. (a) How many of these particles will be scattered greater than 90°? (b) How many will be scattered between 70° and 80°?
- Suppose an electron is accelerated through a 285-V potential. What is the wavelength of the electron, in meters, after undergoing the acceleration?3. A beam of protons, each with energy E = 20 MeV, falls on a potential step of 40 MeV. Graph the probability of finding protons at values of x> 0, for x = 0 at x = 5 fm (Assume | A|^2 = 1).Electrons are fired at a rectangular potential energy barrier, once every 149 ms. If the barrier is 2.55 nm thick and has a height that exceeds the energy of the incident electrons by exactly 712 meV, how long on average would you expect to wait for one electron to pass through the barrier?