Please help me understand how to solve this, don\'t just give me the answer with
ID: 1380012 • Letter: P
Question
Please help me understand how to solve this, don't just give me the answer with no explanation.
You have been able to get a part-time job in a University laboratory. The group is planning a set of experiments to study the forces between nuclei in order 10 understand the energy output of the Sun. To do this experiment, you shoot alpha particles from a Van de Graaf accelerator at a sheet of lead. The alpha particle is the nucleus of a helium atom and is made of 2 protons and 2 neutrons. The lead nucleus is made of 82 protons and 125 neutrons. The mass of the neutron is almost the same as the mass of a proton. To assure that you are actually studying the effects of the nuclear force, an alpha panicle should come into contact uadi a lead nucleus. Assume diat both die alpha particle and the lead nucleus have the shape of a sphere. The alpha particle lias a radius of 1.0 times 10-13 cm and the lead nucleus has a radius 4 times larger. Your boss wants you to make two calculations: What is the minimum speed of such an alpha particle if the icad nucleus is fixed at rest? What is the potential difference between die two ends of the Van de Graaf accelerator if the alpha panicle starts from rest at one end (from a bottle of helium gas)?Explanation / Answer
For the minimum approach speed, all initial kinetic energy will be converted into electrostatic potential energy when the two are in contact. ==> at contact their centers are 5ra apart. The charges of the alpha particle and the Pb nucleus are 2e and 82e.
==> E.P.E = U = (2e)x(82e) /{(4? eps0)5ra} = m v2/2
==> v= 4.75