Question

Of the total number of atoms in the universe, approximately \(93 \%\) are hydrogen \((\mathrm{H}\), atomic weight \(=1.0 \mathrm{~g} / \mathrm{mole})\) and \(7 \%\) are helium \((\mathrm{He}\), atomic weight \(=4.0 \mathrm{~g} / \mathrm{mole})\). What percentage of the universe by weight is hydrogen?

Short answer

The universe is approximately 76.86% hydrogen by weight.

Step-by-step solution

Calculate the weighted percentage of hydrogen and helium atoms

Using the percentage of atoms and the atomic weights provided, we can calculate the weighted percentage of hydrogen and helium atoms in the universe. For hydrogen: Weighted percentage = (percentage of atoms) × (atomic weight) Weighted percentage of hydrogen = (93%) × (1.0 g/mole) = 93 g/mole For helium: Weighted percentage = (percentage of atoms) × (atomic weight) Weighted percentage of helium = (7%) × (4.0 g/mole) = 28 g/mole

Calculate the total weight of hydrogen and helium in the universe

The total weight of hydrogen and helium in the universe is the sum of the weighted percentages of hydrogen and helium: Total weight = Weighted_percentage_of_hydrogen + Weighted_percentage_of_helium Total weight = 93 g/mole (hydrogen) + 28 g/mole (helium) = 121 g/mole

Calculate the percentage of hydrogen by weight

Now that we have the total weight of hydrogen and helium in the universe, we can find the percentage of hydrogen by weight using the following formula: Percentage of hydrogen (by weight) = (Weighted percentage of hydrogen) / (Total weight) × 100 Percentage of hydrogen (by weight) = (93 g/mole) / (121 g/mole) × 100 ≈ 76.86% So, the universe is approximately 76.86% hydrogen by weight.

Key concepts

Hydrogen in Universe

Hydrogen is the most abundant element in the universe. It makes up approximately 93% of all the atoms present. This prevalence is vital for the composition and structure of the universe. Hydrogen atoms serve as the building blocks for more complex elements through nuclear fusion. During this process, hydrogen atoms combine to form helium and release energy.

• Hydrogen is crucial for star formation.
• It has an atomic weight of 1.0 g/mole.
• Essential for the formation of other elements in stars.

Understanding the abundance of hydrogen helps explain the dynamics and life cycle of stars, which is central in the field of astronomy. Moreover, due to its light weight, hydrogen largely influences the universe's mass distribution.

Helium Atomic Weight

Helium is the second most abundant element in the universe. It comprises about 7% of the atomic makeup of the cosmos. Despite being the second most common element, helium is significantly heavier than hydrogen. Its atomic weight is 4.0 g/mole, four times that of hydrogen.

• Produced in the cores of stars via nuclear fusion.
• Heavier atomic weight significantly affects its contribution by mass.
• Key element in studying the early universe, often used in twin theories concerning the universe's origin.

The birth of helium occurs mainly in stars, where it forms from hydrogen under high temperatures and pressures. This transformation is critical for our sun's energy production and the life span of many other stars.

Universe by Weight

When you examine the universe's composition by weight, hydrogen and helium are dominant. Atomic weight plays a key role in how much an element contributes to the universe's mass. Since hydrogen is lighter but more abundant, it takes up a smaller portion of the total universe by weight compared to helium, which is heavier.

• Hydrogen accounts for roughly 76.86% of the universe by weight.
• Helium, while less abundant, carries more weight per atom than hydrogen.
• Heavier elements are far less abundant but significantly impact calculated cosmic masses.

This differing weight distribution is because of the difference in atomic weights and not merely the number of atoms. The lighter weight of hydrogen contributes to its larger presence though significantly balanced by helium's heavier atomic weight.

Percentage Calculations

Calculating percentages by weight in the universe helps us understand the relative contributions of elements like hydrogen and helium. The calculation involves multiplying the percentage abundance of an element by its atomic weight. For example:For hydrogen:- Multiply 93% (abundance) by 1.0 g/mole (atomic weight) to get 93 g/mole.For helium:- Multiply 7% (abundance) by 4.0 g/mole (atomic weight) to get 28 g/mole.To find hydrogen's percentage by weight in the universe, sum these contributions to attain the total weight (121 g/mole) and calculate:\[\text{Percentage of hydrogen} = \left(\frac{93 \text{ g/mole}}{121 \text{ g/mole}}\right) \times 100 \approx 76.86\%\]

• Ensures accurate representation of element contribution.
• Key for understanding cosmic chemical makeup.
• Facilitates further study in cosmic and nuclear physics.

These calculations form the foundation for understanding vast cosmic compositions, from star bodies to entire galaxies.