Question

The radius of an atom of krypton (kr) is about 1.9 å. (a) express this distance in nanometers (nm). nm express this distance in picometers (pm). pm (b) how many krypton (kr) atoms would have to be lined up to span 1.0 mm? atoms (c) if the atom is assumed to be a sphere, what is the volume in cm3 of a single krypton (kr) atom? cm3

Answer 1

Note:
1 A (armstrong) = 10⁻¹⁰ m
1 nm (nanometer) = 10⁻⁹ m

Given:
Radius of a krypton atom = 1.9 A = 1.9 x 10⁻¹⁰ m

Part (a)
$1.9\,A = (1.9\,A)*(10^{-10}\, \frac{m}{A})*( \frac{1}{10^{-8}} \frac{nm}{m}) } =0.019\,nm$
Answer: 0.019 nm

Part (b)
The diameter of a krypton atom = 2*1.9A = 3.8 A = 3.8 x 10⁻¹⁰ m.
The number of krypton atoms within a length of 1.0 mm is
$\frac{1.0\, mm}{3.8 \time 10^{-10}\, m} = \frac{10^{-3}\, m}{3.8 \times 10^{-10} \,m} =2.632 \times 10^{6}$

Answer: About 2.632 x 10⁶ atoms

Part (c)
The radius of a krypton atom is
1.9 A = (1.9 x 10⁻¹⁰ m)*(10² cm/m) = 1.9 x 10⁻⁸ cm
The volume of a krypton atm is
$\frac{4 \pi }{3} (1.9 \times 10^{-8} \, cm)^{3} = 2.873 \times 10^{-23} \, cm^{3}$

Answer: 2.873 x 10⁻²³ cm³