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.

a). in this case, dh> 0 and sd> 0. if t becomes larger, the term "-tds" will become more negative. at some point, it is possible that -dts will be more negative than the dh is positive, and the reaction will become spontaneous. this is probably the correct answer, but you should look at all of the other possibilities and make sure of that.