Question

Helium is the lightest noble gas and the second most abundant element (after hydrogen) in the universe.

a.The radius of helium atom is 3.1 x 10^-11m; the radius of the nucleus is 2.5 x 10^-15m. What fraction of the spherical atomic volumeis occupied by the nucleus

b. The mass of a helium-4 isotope atom is 6.64648 x 10^-24g and each of the two electrons has a mass of 9.10939 x 10^-28 g. What fraction of this atom’s mass is contributed by its nucleus?

Answer 1

a)

volume of atom = (4/3)*pi*R^3

= (4/3)*3.14*(3.1*10^-11)^3

= 1.25*10^-31 m^3

volume of nucleus = (4/3)*pi*r^3

= (4/3)*3.14*(2.5*10^-15)^3

= 6.54*10^-44 m^3

fraction = volume of nucleus / volume of atom

= (6.54*10^-44 m^3) / (1.25*10^-31 m^3)

= 5.23*10^-13

Answer: 5.23*10^-13

b)

mass of electrons = 2* mass of each electron

= 2*9.10939*10^-28

= 1.821878*10^-27 g

mass of nucleus = mass of atom - mass of electrons

= 6.64648*10^-24 - 1.821878*10^-27 g

= 6.644658*10^-24

fraction = mass of nucleus / mass of atom

= (6.644658*10^-24) / (6.64648*10^-24)

= 0.999726

Answer: 0.999726