Chapter 2: Q125CP (page 85)

Helium is the lightest noble gas and the second most abundant element (after hydrogen) in the universe.
(a) The radius of a helium atom is 3.1×10^-11m; the radius of its nucleus is 2.5×10^-15 m. What fraction of the spherical atomic volume is occupied by the nucleus (V of a sphere =4/3 πr³)?
(b) The mass of a helium-4 atom is 6.64648X10^-24 g, and each of its two electrons has a mass of 9.10939×10^-28 g. What fraction of this atom's mass is contributed by its nucleus?

Short Answer

Expert verified

The fraction of the spherical atomic volume is $V = 5 . 2410^{- 13} or 5 . 2410^{- 10} percent$
The fraction of the atom mass is $m = 0.999726 or 99.9726 percent$

Step by step solution

a. Step 1: Finding the fraction of the spherical atomic volume

The radius of the helium and nucleus can be given as,

$r_{1} = 2.5 \times 10^{- 15} r = 3.1 \times 10^{- 11} v_{1} (nucleus) = \frac{4}{3} {r_{1}}^{3} II v_{1} (nucleus) = \frac{4}{3} {(2.5 \times 10^{- 15})}^{3} ∥ v_{1} (nucleus) = 6.54 \times 10^{- 44} v (atom) \frac{4}{3} {r_{}}^{3} II v (atom) \frac{4}{3} {(3.1 \times 10^{- 11})}^{3} II v_{1} (atom) = 1.25 \times 10^{- 31} fraction (v) = \frac{v_{1}}{v} fraction (v) = \frac{6.54 \times 10^{- 44}}{1.25 \times 10^{- 31}} fraction (v) = 5.24 \times 10^{- 13} or 5.24 \times 10^{- 11} percent$

b. Step 2: Finding the fraction of this atom's mass is contributed by its nucleus

The mass of the atom and electron can be denoted as,

$m (atom) = 6.64648 \times 10^{- 24} g m_{1} (electron) = 9 . 1093910^{- 28} g$

The electron contains 2 electrons and masses can be sum up.

role="math" localid="1657107198424" $m_{1} (electrons) = 1.8219 \times 10^{- 27} g m_{2} (nucleus) = m - m_{1} m_{2} (nucleus) = 6.64648 \times 10^{- 24} - 1.821910 \times 10^{- 27} m_{2} (nucleus) = 6.64466 \times 10^{- 24} g fraction = \frac{m_{2}}{m} fraction = \frac{6.64466 \times 10^{- 24}}{6.64648 \times 10^{- 24}} fraction (m) = 0.999726 or 99.9726 %$

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Short Answer

Step by step solution

a. Step 1: Finding the fraction of the spherical atomic volume

b. Step 2: Finding the fraction of this atom's mass is contributed by its nucleus

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