Homework 14. Helium Synthesis

Name: ________________________ DUE 12/04 ID number: ________________________

When the Universe was just 3 minutes old, atoms had not yet formed. However, the particles which make up the nuclei of atoms were present; in particular, the Universe contained protons and neutrons. At this time, protons outnumbered neutrons by a ratio of 7:1 -- in other words, there were 7 protons for each neutron. By the time the Universe was a quarter of an hour old, all these neutrons had combined with protons to make Helium nuclei.

Show that the result of this process is a mixture in which 75% of the mass is Hydrogen nuclei and the other 25% is Helium nuclei. Using your own words, explain the reasoning behind your answer; this explanation is an important part of the assignment, and you must include an explanation to get credit.

(Hints: a Hydrogen nucleus is just a single proton, while a Helium nucleus contains two protons and two neutrons. For the purpose of this assignment, assume that a neutron has the same mass as a proton, and that a Helium nucleus has four times the mass of a Hydrogen nucleus. Don't confuse this process with Hydrogen burning in stars! In stars, protons are transformed into neutrons, while here the ratio of neutrons to protons does not change.)

Continue on the back.

Joshua E. Barnes (barnes@ifa.hawaii.edu)

Last modified: November 27, 2001