The mass composition of universe may be given as \(90 \% \mathrm{H}_{2}\) and \(10 \% \mathrm{He}\). The average molecular mass of universe should be (a) \(2.20\) (b) \(2.10\) (c) \(3.80\) (d) \(3.64\)

Understanding the molecular mass of elements is essential in chemistry, and hydrogen is no exception. Hydrogen, represented as H on the periodic table, is the lightest and most abundant chemical element. When we talk about its molecular mass, we're referring to the mass of a single atom of hydrogen. However, hydrogen commonly exists as a diatomic molecule, meaning it naturally pairs up with another hydrogen atom to form H₂.

The molecular mass of a hydrogen atom is approximately 1 atomic mass unit (u), which is a standard unit used to express atomic and molecular masses. For H₂, this means the molecular mass would be roughly 2u. However, in many calculations—particularly in this context of the universe’s mass composition—we consider only one atom of hydrogen, so we use 1u for simplicity.

Helium (He) is known for being not just a party balloon filler, but also an important element in various scientific applications. Its molecular mass is key to many computations, including astrophysics and gas law calculations. A single helium atom has a molecular mass of 4 atomic mass units (u), which makes it more substantial than hydrogen but still one of the lightest elements.

In the context of this exercise, we only deal with the mass of helium's single atoms, and therefore, we will use the atomic mass of 4u. The distinct gap in mass between hydrogen and helium affects the average molecular mass of a system, like the universe, especially because helium is the second-most abundant element following hydrogen.

Delving into the makeup of the universe is a matter of cosmic proportions! The universe's mass composition refers to the relative abundance of elements. Astoundingly, about 90% of the visible universe is hydrogen, the simplest and most primitive element, which aligns with the predictions of the Big Bang theory. Helium accounts for about 10%, which resulted from the fusion of hydrogen in the early moments post-Big Bang.

These figures are significant for calculations involving cosmic matter. For instance, when determining the average molecular mass of the universe—an essential factor for astronomers and physicists—we use these mass compositions. Any calculation must take into account the predominance of hydrogen (90%) versus helium (10%) to draw accurate conclusions about the universe's overall molecular mass.

The atomic mass unit (u) is a fundamental concept when it comes to discussing molecular masses. It gives us a way to express the mass of atoms and molecules on a scale that's convenient for chemical and physical equations. An atomic mass unit is defined as one-twelfth of the mass of a carbon-12 atom, which is approximately equal to 1.66053904 × 10^-24 grams.

Using this standard unit ensures that scientists and students around the world can communicate these masses in a consistent manner. It allows us to understand quickly that helium, with its 4u, is heavier than hydrogen at 1u, without having to wade through complex conversions and massive numbers typical of grams or kilograms. Moreover, in our exercise, we have used atomic mass units to derive the average molecular mass of the universe.