The sun is a hot plasma (ionized matter) with its inner core at a temperature exceeding 10⁷ K, and its outer surface at a temperature of about 6000 K. At these high temperatures no substance remains in a solid or liquid phase. In what range do you expect the mass density of the sun to be ? In the range of densities of solids and liquids or gases ? Check if your guess is correct from the following data: mass of the sun = 2.0 x 10³⁰kg, radius of the sun = 7.0 x 10⁸ m.

The correct option is 1.437 x 10²⁷ m³ and 1.4 x10³ kg m⁻³.

To find the density of the Sun, we need to first calculate its volume and then use its given mass to find the mass density.

Step 1: Calculate the volume of the Sun
The Sun is assumed to be a sphere of radius $R$. The volume $V$ of a sphere is given by the formula:

$V=\frac{4}{3}\pi R^3$
Given data:
Mass of the Sun, $M=2.0\times {10}^{30}\text{kg}$
Radius of the Sun, $R=7.0\times {10}^8\text{m}$

Substituting the value of $R$ into the volume equation:

$V=\frac{4}{3}\times 3.1416\times {(7.0\times {10}^8)}^3$

$V=\frac{4}{3}\times 3.1416\times 343\times {10}^{24}$

$V\approx 1.437\times {10}^{27}{\text{m}}^3$

Step 2: Calculate the mass density of the Sun
The mass density $\rho$ is defined as mass per unit volume:

$\rho =\frac{M}{V}$
Substituting the values of $M$ and $V$:

$\rho =\frac{2.0\times {10}^{30}}{1.437\times {10}^{27}}$

$\rho \approx 1.39\times {10}^3{\text{kg m}}^{-3}\approx 1.4\times {10}^3{\text{kg m}}^{-3}$

Step 3: Comparison with solids, liquids, and gases
The calculated density of the Sun ($1.4\times {10}^3{\text{kg m}}^{-3}$) is in the range of the densities of solids and liquids (for instance, the density of water is $1.0\times {10}^3{\text{kg m}}^{-3}$), which is much higher than the typical densities of gases at standard temperature and pressure.
Even though the high temperatures of the Sun prevent atoms from forming stable solid or liquid phases, the immense gravitational pull at the core compresses the ionized matter (plasma) tightly together, resulting in a density comparable to that of solids and liquids.