Hello, I'm an AS student and probably going to study A2. I was wondering if someone tell me how to work out these questions, step by step? Relationship between Radius of Nucleus And Mass Number 1. By assuming that the density of the nucleus is the same for all elements in the periodic table, show that the radius of the nucleus of any element satisfies R α A^(1/3) α = directly proportional where A is the mass number of the nucleus. Assume nucleus is a spherical (4/3)π(r)^3 Determining the approximate size of the Nucleus Rutherford was able to estimate the size of the nucleus by firing a stream of alpha particles at a thin layer of gold leaf a few atoms thick. Consider an alpha particle is traveling towards the Gold nucleas. The alpha particle is positively charged and the Gold nucleus is postively charged. Therefore, for head on collisions between the alpha and the nucleus, there will be a time when all of the Kinetic energy of the alpha particles is converted into electrical potential energy (the alpha particle gets slower and slower as it gets closer to the nucleus before momentarily stopping, then it gets repelled back in the same direction that it came from. This is similar to when you throw a ball into the air. The balls velocity decreases as it travels upwards until it momentarily stops at the point when all the kinetic energy has been converted into gravitational potential energy. The ball then falls back to the ground). It is possible to determine the distance between the nucleus and the alpha particle at the point where all the kinetic energy has been converted into electrical potential energy. This distance provides an estimate for size of the nucleus. Obviously, the fast the initial velocity of the alpha particle, the closer the alpha particle will get tothe nucleus and the more accurate the estimated size of the nucleus will be. 2. Your task is to derive a general expression for the radius of a nuclus of atomic number Z in terms of the initial velocity of the alpha particle. You must then estimate the size of the nucleus by assuming that the initial velocity of the alpha particle is 2 x 10^7 m/s. Hint: An expression for the electrical potential energy VE can be inferred from the relation: FE = - (dVE / dr) where FE is the Coulomb Force acting between two charges Q1 and Q2 seperated by a distance r: FE = (1/4π weird symbol) x (Q1Q2 / r^2) Electrical potential energy = (1/4πweirdsymbol) x (Q1Q2/r) NOTE: Weird symbol looks like a euro sign and has a small zero next to it. I'm not sure what it is. c: 1. I'm confused as to how you show that the radius of the nucleus of any element is satisfied. I used Gold, and I did: Mass number of Gold = 197 R α 197^(1/3) R α 5.819 After that, I'm a little lost. Do I do the following? (4/3) x π x 5.819^3 = 825.19 That seems wrong. 2. This one, I'm just very lost. I don't know where to start!