using data in table 6.5, calculate the densities of (spherical) atoms of potassium and calcium and compare to the listed densitites of these metals
K=39.10 amu, .231 nm (atomic radius)
Ca= 40.08 amu, .197nm (atomic radius)
To calculate the densities of the spherical atoms of potassium (K) and calcium (Ca), we will use the formula:
Density = (Atomic Mass) / (Volume)
Let's calculate the volumes first.
To calculate the volume of a sphere, we will use the formula:
Volume = (4/3) * π * (radius)^3
For potassium (K):
Given:
Atomic Mass (K) = 39.10 amu
Atomic Radius (K) = 0.231 nm
Converting the atomic radius from nanometers to centimeters:
1 nm = 1 x 10^-7 cm
0.231 nm = 0.231 x 10^-7 cm = 2.31 x 10^-8 cm
Using the formula for the volume of a sphere:
Volume (K) = (4/3) * π * (2.31 x 10^-8 cm)^3
Now calculate the volume of potassium.
For calcium (Ca):
Given:
Atomic Mass (Ca) = 40.08 amu
Atomic Radius (Ca) = 0.197 nm
Converting the atomic radius from nanometers to centimeters:
0.197 nm = 0.197 x 10^-7 cm = 1.97 x 10^-8 cm
Using the formula for the volume of a sphere:
Volume (Ca) = (4/3) * π * (1.97 x 10^-8 cm)^3
Now calculate the volume of calcium.
Once we have the volumes, we can calculate the densities using the given atomic masses.
Density(K) = Atomic Mass (K) / Volume (K)
Density(Ca) = Atomic Mass (Ca) / Volume (Ca)
Finally, we can compare the calculated densities with the listed densities of these metals.