Question

What would be the radius of the earth if it had its actual mass but had the density of nuclei?

Answer 1

If the Earth had the density of a nucleus, its radius would be only about 200 meters compared to the actual radius of approximately 6.4 x 10^6 meters.

Step-by-step explanation:

Protons and neutrons, collectively called nucleons, are packed together tightly in a nucleus. With a radius of about 10-15 meters, a nucleus is quite small compared to the radius of the entire atom, which is about 10-10 meters. Nuclei are extremely dense compared to bulk matter, averaging 1.8 × 1014 grams per cubic centimeter. If the earth's density were equal to the average nuclear density, the earth's radius would be only about 200 meters (earth's actual radius is approximately 6.4 x 106 meters, 30,000 times larger).

Answer 2

162.3 m

Step-by-step explanation:

The mass of the Earth is

`M=5.98\cdot 10^(24) kg`

while the density of nuclei is

`d=3.345\cdot 10^(17)kg/m^3`

So we can find the volume of the Earth if it had this density:

`V=(M)/(d)=(5.98\cdot 10^(24)kg)/(3.345\cdot 10^(17)kg/m^3)=1.79\cdot 10^(7) m^3`

Assuming the Earth is a perfect sphere, its volume is given by

`V=(4)/(3)\pi r^3`

where r is the radius. Solving for r, we find

`r=\sqrt[3]{(3V)/(4\pi)}=\sqrt[3]{(3(1.79\cdot 10^7 m^3))/(4\pi)}=162.3 m`