earth has a mass of 5.98 x 10 24 kg. the average mass of the atoms that make up earth is 40 u. how many atoms are there in earth?
The Correct Answer and Explanation is :
To calculate the number of atoms in Earth, we can follow these steps:
Given:
- Mass of Earth (M) = (5.98 \times 10^{24} \, \text{kg})
- Average atomic mass (m) = (40 \, \text{u}) (unified atomic mass units)
Conversion:
- Convert the atomic mass from atomic mass units to kilograms:
[
1 \, \text{u} = 1.66 \times 10^{-27} \, \text{kg}
]
Thus,
[
m = 40 \, \text{u} \times 1.66 \times 10^{-27} \, \text{kg/u} = 6.64 \times 10^{-26} \, \text{kg}
] - Calculate the number of atoms (N):
The number of atoms can be calculated using the formula:
[
N = \frac{M}{m}
]
Substituting the values:
[
N = \frac{5.98 \times 10^{24} \, \text{kg}}{6.64 \times 10^{-26} \, \text{kg}} \approx 9.00 \times 10^{49}
]
Final Answer:
The estimated number of atoms in Earth is approximately (9.00 \times 10^{49}) atoms.
Explanation:
The calculation above provides a fundamental understanding of how the mass of a planet can be translated into the number of atoms it contains. The mass of Earth, approximately (5.98 \times 10^{24} \, \text{kg}), reflects the total weight of all the materials, primarily rock and metal, that compose it.
In atomic physics, the unified atomic mass unit (u) serves as a standard for measuring atomic and molecular masses. The average atomic mass of Earth’s atoms is given as 40 u, indicating that Earth’s atoms are primarily composed of elements like silicon, aluminum, and iron, which have relatively high atomic masses.
Converting atomic mass into kilograms allows us to employ standard mass units for our calculations. By dividing the total mass of the Earth by the mass of a single atom, we can derive the total number of atoms present. This massive number, (9.00 \times 10^{49}), illustrates the vastness of matter even in a relatively small object compared to the universe, emphasizing the incredible scale and complexity of the planet we inhabit.