Outline, with reference to star formation, what is meant by the Jeans criterion.

In the proton–proton cycle, four hydrogen nuclei fuse to produce one nucleus of helium releasing a total of 4.3 × 10^–12 J of energy. The Sun will spend 10¹⁰ years on the main sequence. It may be assumed that during this time the Sun maintains a constant luminosity of 3.8 × 10²⁶ W.

Show that the total mass of hydrogen that is converted into helium while the Sun is on the main sequence is 2 × 10²⁹ kg.

Massive stars that have left the main sequence have a layered structure with different chemical elements in different layers. Discuss this structure by reference to the nuclear reactions taking place in such stars.

a star will form out of a cloud of gas

when the gravitational potential energy of the cloud exceeds the total random kinetic energy of the particles of the cloud
OR
the mass exceeds a critical mass for a particular radius and temperature

[2 marks]

number of reactions is \(\frac{{{{10}^{10}} \times 365 \times 24 \times 3600 \times 3.8 \times {{10}^{26}}}}{{4.3 \times {{10}^{ - 12}}}} = 2.79 \times {10^{55}}\)

H mass used is \(2.79 \times {10^{55}} \times 4 \times 1.67 \times {10^{ - 27}} = 1.86 \times {10^{29}}\) «kg»

[2 marks]

nuclear fusion reactions produce ever heavier elements depending on the mass of the star / temperature of the core

the elements / nuclear reactions arrange themselves in layers, heaviest at the core lightest in the envelope

[2 marks]