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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