In the Sun, hydrogen makes up 90 % of the atoms,...

In the Sun, hydrogen makes up $90 \%$ of the atoms, corresponding to $75 \%$ of its mass. Iron and other elements with atomic weights of about 56 make up $0.001 \%$ of the atoms, while silicon and other elements with atomic weights of about 28 make up $0.01 \%$ of the atoms. These represent the percentage of atoms, not the fraction of the mass. If Jupiter has the same proportions of atoms in its interior, what would the total mass of Jupiter's iron- and silicon-like atoms be? Compare the masses you find to the mass of the Earth.

Key Concepts

Comparative Planetary Mass Analysis

Once the mass fraction of heavy elements is computed, comparing these derived masses to that of another planetary body, such as the Earth, helps put these numbers in perspective. This method of scaling and comparison is essential in planetary science, as it provides insights into the formation, structure, and evolution of planets relative to each other.

Planetary Interior Composition

Understanding the composition of a planetary interior involves using the ratios of different atoms as determined by astronomical observations or models. For gas giants like Jupiter, assuming similar proportions of atoms as found in the Sun allows scientists to apply stellar composition techniques to deduce the mass of particular heavy elements contained within.

Atomic Abundance

This concept distinguishes between the number fraction of atoms (how many atoms of each type are present) and the mass fraction (what percentage of the overall mass is contributed by those atoms). In astrophysical objects, an element can be numerically dominant yet contribute less to the total mass if its atoms have a lower atomic mass.

Mass Fraction Conversion

When given percentages by number, it is important to correctly convert them into mass fractions for accurate comparisons. This involves multiplying the number fraction of an element by its atomic weight relative to other elements in the mixture. In the case of the Sun or Jupiter, low-abundance but high-mass atoms like iron contribute more significantly to the mass even if they are extremely rare in number.

Atomic Weight and Relative Mass

Atomic weight, which indicates how much mass an atom has compared to hydrogen, is crucial when moving from a count of atoms to a calculation of mass. Heavy elements such as iron or silicon, despite making up a small percentage of the total atoms, each pack considerably more mass per atom than lighter elements like hydrogen, thereby altering the overall mass distribution in a star or planet.

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