# Primary Nucleosynthesis

### Problem 1

Find the ratio of neutrons to protons number densities in the case of thermal equilibrium between them.

### Problem 2

Up to what temperature can the reaction $n\nu_e\leftrightarrow pe^-$ support thermal equilibrium between protons and neutrons in the expanding Universe

### Problem 3

Determine the ratio $n_n/n_p$ at the temperature of freeze-out.

### Problem 4

Determine the age of Universe when it reached the temperature of freeze-out.

### Problem 5

At what temperature and at what time did efficient deuterium synthesis start?

### Problem 6

Determine the time period during which the synthesis of light elements took place.

### Problem 7

Determine the ratio of neutrons to protons number densities at temperature interval from the freeze-out to the creation of deuterium.

### Problem 8

Determine the relative abundance of ${}^4He$ in the Universe

### Problem 9

How many helium atoms are there for each hydrogen atom?

### Problem 10

What changes in relative ${}^4 He$ abundance would be caused by

a) decreasing of average neutron lifetime $\tau_n$;

b) decreasing or increasing of the temperature of freeze-out $T_f$?

### Problem 11

What nuclear reactions provided the ${}^4 He$ synthesis in the early Universe?

### Problem 12

Why is synthesis of elements heavier than ${}^7 Li$ suppressed in the early Universe?

### Problem 13

In our Universe the neutron half-value period (the life-time) approximately equals to 600 seconds. What would the relative helium abundance be if the neutron life-time decreased down to 100 seconds?

### Problem 14

At what temperature in Universe did the synthesis reactions stop?