Although the earth was formed from the same interstellar material as the sun, there is little elemental hydrogen \(\left(\mathrm{H}_{2}\right)\) in the earth's atmosphere. Explain.

Firstly, let's consider the properties of hydrogen. Hydrogen is the lightest and most abundant element in the universe, with an atomic mass of about 1.0079 atomic mass units (amu). Being a light element, hydrogen has a low density and a high tendency to escape into space when not bound to other elements.

The Earth's atmosphere is made up of a variety of gases, with the primary composition being nitrogen (78%), oxygen (21%), and trace amounts of other gases such as argon, carbon dioxide, and water vapor. Noticeably, hydrogen is not present in significant amounts.

Due to its low mass, hydrogen has a higher average speed at a given temperature compared to heavier gases. As a result, it can more easily reach escape velocity and escape Earth's gravitational pull. Over time, a significant amount of hydrogen has escaped Earth's atmosphere, resulting in its low concentration today.

Additionally, hydrogen can combine with other elements to form compounds, such as water (H2O). This process further reduces the elemental hydrogen concentration in the atmosphere since it is now bound to other elements.

The Sun, being significantly more massive than Earth, has a much stronger gravitational pull. This allows it to retain a large amount of hydrogen, which fuels the nuclear fusion reactions at its core. Furthermore, the high temperature and pressure in the Sun prevent hydrogen from forming compounds with other elements, allowing it to remain in its elemental form. In conclusion, Earth's atmosphere contains little elemental hydrogen due to its low mass and tendency to escape the planet's gravitational pull, as well as its propensity to form compounds with other elements. Despite being formed from the same interstellar material as the Sun, Earth's size and atmospheric conditions have led to these differences in hydrogen concentration.