Why Is the Number of Nucleons in Earth Incorrect?

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SUMMARY

The calculation of the number of nucleons in Earth, based on its diameter of 12.70 km and average density of 5.5 grams per cubic centimeter, yields an incorrect result. The computed mass of Earth, approximately 5.899 x 1015 kg, leads to an estimated 3.53 x 1042 nucleons. The error arises from the incorrect assumption regarding Earth's diameter, which is significantly larger than stated, leading to a flawed volume calculation. Accurate measurements of Earth's diameter and density are essential for precise nucleon estimations.

PREREQUISITES
  • Understanding of basic physics concepts, including mass, volume, and density.
  • Familiarity with the formula for calculating the volume of a sphere: Volume = 4/3πr3.
  • Knowledge of nucleon mass, specifically 1.67 x 10-27 kilograms.
  • Ability to perform unit conversions between grams per cubic centimeter and kilograms per cubic meter.
NEXT STEPS
  • Research accurate measurements of Earth's diameter and density for improved calculations.
  • Explore the implications of using incorrect physical constants in scientific calculations.
  • Learn about the significance of nucleons in atomic structure and their role in mass calculations.
  • Investigate common errors in physics homework problems and how to avoid them.
USEFUL FOR

Students studying physics, educators teaching about mass and density, and anyone interested in understanding the calculations related to Earth's physical properties.

hndalama
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Homework Statement


The Earth is about 12.70 km in diameter. The Earth’s average density is about 5.5 grams cubic centimeter. A nucleon (the main constituent of an atomic nucleus) has a mass of about 1.67 x 10⁻²⁷ kilograms. If the Earth’s mass is entirely due to its nucleons, how many nucleons are in the Earth?

Homework Equations


Volume = 4/3pi*r3

The Attempt at a Solution


radius =6350m
volume = 4/3pi*(6350)3 = 1.07 *1012
density =5.5g/cm3 =5500kg/m3
Earth's mass = density*volume
=5500kg/m3 * 1.07 *1012
=5.899 *1015 kg

number of nucleons= 5.899 *1015 kg / 1.67 x 10⁻²⁷
= 3.53 * 1042

This answer is wrong but why is it wrong?
 
Last edited:
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hndalama said:
The Earth is about 12.70 km in diameter.
Uh ... seriously?
 
phinds said:
Uh ... seriously?
lol, thank you, I thought something was fishy :smile:
 

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