Summary The student explores how helium was made in the Big Bang.

Background and Theory

Very little helium is made in stars. Yet the universe is roughly 1/4 helium and 3/4 hydrogen by mass. How can this be? Early in the Big Bang the Universe was hot and dense (like the core of a star) and protons could fuse together to make some helium. The fact that the Universe is 1/4 helium is very good evidence for the existence of the Big Bang and a hot early Universe.

Procedure

Print the worksheet
1. In the very early Universe, (before 0.01 seconds), the temperature was too high for even protons and neutrons to exist. Certainly, nuclei of atoms, which require protons and neutrons, could not exist. If nuclei did form, high energy radiation (gamma rays), tore them apart. Once the Universe expanded and cooled to 100 billion degrees, neutrons and protons could persist. Not only that, but they could switch back and forth:

neutron + neutrino -> proton + electron
neutron + positron -> proton + anti-neutrino
neutron -> proton + neutrino + electron

The total number of particles stays the same but the fraction which are neutrons depends on the temperature, (and nothing else). Another way to say this is that the neutrons and protons numbers are in thermal equilibrium. To stay in thermal equilibrium all of the reactions above need to be occurring frequently.

Neutrons require more energy to make because they are heavier than protons (E = m c2). As the temperature drops, there is less energy available, and the reactions begin to favor protons (see Table 1).

Table 1: Neutron fraction at Equilibrium for a given Temperature
Temperature Equilibrium Neutron Fraction Equilibrium Reaction Speed
100,000,000,000 K 50/100 Fast
30,000,000,000 K 37/100 Slow
10,000,000,000 K 18/100 Stopped
3,000,000,000 K 1/100 Stopped
1,700,000,000 K 0.01/100 Stopped
1,200,000,000 K 0.0004/100 Stopped
1,000,000,000 K 0.00003/100 Stopped
900,000,000 K 0.000006/100 Stopped

On the worksheet there are 100 particles (protons or neutrons) in a box at various times. Using the Equilibrium fractions given in Table 1, indicate how many are neutrons at 0.1 seconds and 1 second by marking the circles. 0.01 seconds is already marked. Use version 1 to indicate the number of neutrons at 50 seconds, 100 seconds, 150 seconds and 200 seconds.

2. If the Equilibrium reactions have stopped then neutrons simply decay:

neutron -> proton + neutrino + electron

The decay has a half life of 600 seconds. In 600 seconds, a neutron is as likely to turn into a proton as it is to stay a neutron. This can be simulated by tossing a coin. If it lands heads up, the neutron has turned into a proton. The chance of decaying in 50 seconds is much less, one in 16. The neutron will turn into a proton if four coins land heads up.

Take the neutrons present at 1 second and for version 2 of the Big Bang determine if each neutron makes it to 50 seconds and mark it in if it does. Take the neutrons present at 50 seconds and repeat the procedure again for 50 seconds later (100 seconds). Evolve your set of neutrons to 200 seconds this way. You should have a reasonable number of neutrons left at 200 seconds.

3. At 200 seconds the Universe is cool enough that deuterium can form, a necessary step in forming helium. All deuterium is converted quickly into helium. Draw circles around groups of two neutrons and two protons at 200 seconds (version 2). If you have any left over neutrons draw a circle around it and one proton. This is a deuterium nucleus. Once neutrons are inside a nucleus they stop decaying.

4. Repeats step 2-3 for version 3. This time assume deuterium is able to form at 150 seconds so circle the helium then.