The single proton that forms the nucleus of the hydrogen atom has a radius of approximately 1.0×10−13cm. the hydrogen atom itself has a radius of approximately 52.9 pm what fraction of the space within the atom is occupied by the nucleus?

The answer is

6.8 * 10^-15

The explanation:

1- we have to convert all measurements to the same units:  

Conversions:  

when 1 m = 100 cm  

and 1 m = 10^12 pm  

So,

proton radius: 1.0*10^-13 cm * (1m / 100 cm) = 10^-15 m  

proton volume: 4/3 * pi * r^3 = 4/3 * pi * (10^-15 m)^3 = 4.2 * 10^-45 cu. meters  

and

H atom radius: 52.9 pm * (1m / 10^12 pm) = 5.29 * 10^-11 m  

H atom volume: 4/3 * pi * r^3 = 4/3 * pi * (5.29 * 10^-11 m)^3 = 6.2 × 10^-31 cu. meters  

So,

2- Fraction of space occupied by nucleus = proton volume / H atom volume  

= (4.2 * 10^-45 cu. meters) / (6.2 × 10^-31 cu. meters)  

= 6.8 * 10^-15  

So, the "fraction" would be 6.8 * 10^-15 out of 1.

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