Why Is the Number of Nucleons in Earth Incorrect?

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The discussion centers on calculating the number of nucleons in Earth based on its diameter, density, and the mass of a nucleon. The calculations yield an estimated mass of Earth as approximately 5.899 x 10^15 kg, leading to a calculated number of nucleons around 3.53 x 10^42. However, participants express skepticism about the initial diameter of Earth being cited as 12.70 km, indicating a fundamental error in the assumptions. The discrepancy in the diameter suggests that the calculations are based on incorrect parameters, leading to an inaccurate conclusion. The conversation highlights the importance of using correct values in scientific calculations.
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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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