At the central core of the Sun the density is and the composition is essentially 35% hydrogen by mass and 65% helium. (a) We have to find the density of protons at the Sun’s core. (a) We have to find the ratio of this to the density of particles for an ideal gas at standard conditions of temperature and pressure.

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(a)

At the central core of the Sun the density is and the composition is essentially 35% hydrogen by mass and 65% helium. Therefore, the contribution to the mass density by hydrogen will be

The mass of proton Therefore, the number density of protons at the central core of the Sun will be

.

(b)

The number density of particles in an ideal gas is determined by its pressure and temperature. The ideal gas equation of state is

,

where k is the Boltzmann constant. The standard conditions of pressure and temperature are

Therefore,

And